Package 'astsa'

Description

Contains data sets and scripts for analyzing time series in both the frequency and time domains including state space modeling as well as supporting the texts Time Series Analysis and Its Applications: With R Examples (5th ed, 2025) and Time Series: A Data Analysis Approach Using R, (2nd ed, 2026). Most scripts are designed to need minimal input to produce aesthetically pleasing output for ease of use in live demonstrations and in course work.

Details

Warning

If the package dplyr is loaded, it will mask the base scripts filter and lag (among other things) that a time series analyst uses often. In this case, whenever you analyze time series data, we suggest you either:

(1) Detach it if it's loaded but not being used:

   detach(package:dplyr)

(2) If you want to use it, fix it:

   library(dplyr, exclude = c("filter", "lag"))   # load it without the culprits 
   dlag    = dplyr::lag         # and fix ... 
   dfilter = dplyr::filter      # ... the blunders

then use dlag and dfilter for dplyr scripts
and lag and filter can be use as originally intended.

(3) Or just take back the commands:

   filter = stats::filter
   lag    = stats::lag 

and you can still use these for dpylr:

   dlag    = dplyr::lag
   dfilter = dplyr::filter

(4) Or avoid all of these problems and use data.table instead of dplyr. If you are doing data manipulation, you should know that dplyr is inspired by data.table, but it is much slower and weaker than data.table.

Author(s)

David Stoffer <[email protected]>

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Produces a plot (and a printout) of the sample ACF or PACF. The zero lag value of the ACF is removed.

Usage

acf1(series, max.lag = NULL, plot = TRUE, main = NULL, ylim = NULL, pacf = FALSE,
      ylab = NULL, xlab = NULL, na.action = na.pass, ...)

Arguments

Details

Will print and/or plot the sample ACF or PACF (if pacf=TRUE). The zero lag of the ACF (which is always 1) has been removed. If plot=TRUE, a graph is produced and the values are rounded and listed. If plot=FALSE, no graph is produced and the values are listed but not rounded by the script. The error bounds are approximate white noise bounds, $-1/n \pm 2/\sqrt{n}$; no other option is given.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf2, acfm, ccf2

Examples

acf1(rnorm(100))

acf1(sarima.sim(ar=.9), pacf=TRUE)

acf1(soi, col=2:7, lwd=4, gg=TRUE)

Description

Produces a simultaneous plot (and a printout) of the sample ACF and PACF on the same scale. The zero lag value of the ACF is removed.

Usage

acf2(series, max.lag = NULL, plot = TRUE, main = NULL, ylim = NULL, 
      na.action = na.pass, ...)

Arguments

Details

Will print and/or plot the sample ACF and PACF on the same scale. The zero lag of the ACF (which is always 1) has been removed. If plot=TRUE, a graph is produced and the values are rounded and listed. If plot=FALSE, no graph is produced and the values are listed but not rounded by the script. The error bounds are approximate white noise bounds, $-1/n \pm 2/\sqrt{n}$; no other option is given.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf1, acfm, ccf2

Examples

acf2(rnorm(100))

acf2(rnorm(100), 25, main=NA)   # no title

acf2(rnorm(100), max.lag=5, plot=FALSE)  # print only

acf2(soi, col=2:7, lwd=4, gg=TRUE)

Description

Produces a grid of plots of the sample ACF (diagonal) and CCF (off-diagonal). The values are returned invisibly.

Usage

acfm(series, max.lag = NULL,  na.action = na.pass, ylim = NULL,
      acf.highlight = TRUE, plot = TRUE, ...)

Arguments

Details

Produces a grid of plots of the sample ACF (diagonal) and CCF (off-diagonal). The plots in the grid are estimates of corr{x(t+LAG), y(t)}. Thus x leads y if LAG is positive and x lags y if LAG is negative. If plot is FALSE, then there is no graphic.

Value

The correlations are returned invisibly.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf1, acf2, ccf2

Examples

acfm(diff(log(econ5)), gg=TRUE)

acfm(diff(log(econ5)), 2, plot=FALSE)

Description

Performs a nonparametric bootstrap to obtain the distribution of the AR model parameters.

Usage

ar.boot(series, order.ar, nboot = 500, seed = NULL, plot = TRUE, ...)

Arguments

Details

For a specified series, finds the bootstrap distribution of the Yule-Walker estimates of $\phi_1,\dots,\phi_p$ in the AR model specified by order.ar,

$x_t = \mu + \phi_1 (x_{t-1}-\mu) + \dots + \phi_p (x_{t-p}-\mu) + w_t ,$

where $w_t$ is white noise. The data are centered by the sample mean prior to the bootstrap simulations.

The script displays a number of quantiles of the bootstrapped estimates, the means, the biases, and the root mean squared errors.

Value

Returned invisibly as a list:

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

u = ar.boot(rec, 2)
dev.new()
tspairs(u[[1]], hist=FALSE)   # another view of results
head(u[[1]])       # some booted AR parameters
head(u[[2]][,1:5]) # some booted data

## End(Not run)

Description

Uses Gibbs sampling to fit an AR model to time series data.

Usage

ar.mcmc(xdata, porder, n.iter = 1000, n.warmup = 100, plot = TRUE,  
        prior_var_phi = 50, prior_sig_a = 1, prior_sig_b = 2, ...)

Arguments

Details

Assumes a normal-inverse gamma model,

$x_t = \phi_0 + \phi_1 x_{t-1} + \dots + \phi_p x_{t-p} + \sigma z_t ,$

where $z_t$ is standard Gaussian noise. With $\Phi$ being the (p+1)-dimensional vector of the $\phi$s, the priors are $\Phi \mid \sigma \sim N(0, \sigma^2 V_0)$ and $\sigma^2 \sim IG(a,b)$, where $V_0 = \gamma^2 I$. Defaults are given for the hyperparameters, but the user may choose $(a,b)$ as (prior_sig_a, prior_sig_b) and $\gamma^2$ as prior_var_phi.

The algorithm is efficient and converges quickly. Further details can be found in Chapter 6 of the 5th edition of the Springer text.

Value

In addition to the graphics (if plot is TRUE), the draws of each parameter (phi0, phi1, ..., sigma) are returned invisibly and means, standard deviations, and various quantiles are displayed.

Author(s)

D.S. Stoffer

Source

Based on the script arp.mcmc used in Douc, Moulines, & Stoffer, D. (2014). Nonlinear Time Series: Theory, Methods and Applications with R Examples. CRC press. ISBN 9781466502253.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

u = ar.mcmc(rec, 2)

tspairs(u, hist=FALSE, col.diag=6)  # another view 

tsplot(u, ncol=2, col=4, xlab='Index')  # traces only


## End(Not run)

Description

Data used in Chapter 6 Problems

Format

The format is: Time-Series [1:100] with NA for missing values.

Details

Simulated AR(1) with $\phi=.9$ and $\sigma_w=1$ and ~10% of the values missing at random (in this case, there happen to be 15 missing values). A similar data set can be generated as follows:

x   = sarima.sim(ar=.9, n=100)
u   = sample(c(NA,0), replace=TRUE, size=100, prob=c(.1,.9))
arm = x + u 

Another approach if you want exactly 10 missing values is this:

arms = sarima.sim(ar=.9, n=100)
arms[sample(1:100, size=10)] = NA

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# use type='o' when plotting a series with missing data
par(mfrow=2:1)
tsplot(ar1miss, col=4)
tsplot(ar1miss, col=4, type='o', pch=19)

Description

1000 simulated observations from an ARFIMA(1, 1, 0) model with $\phi = .75$ and $d = .4$.

Format

The format is: Time-Series [1:1000] from 1 to 1000: -0.0294 0.7487 -0.3386 -1.0332 -0.2627 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

par(mfrow=2:1)
tsplot(arf, col=4, main='ARFIMA')
acf1(arf, col=4, main=NA)

Description

For a given ARMA model (including seasonal models), reports whether the model is causal, invertible, or (approximately) over-parameterized.

Usage

arma.check(ar = 0, ma = 0, sar = NULL, sma = NULL, S = NULL, redtol = 0.1,
           plot.it = FALSE, ...)

Arguments

Details

Causality and invertibility are checked first. If either one or both are reported, checking is stopped.

If the model is causal and invertible, a warning for (possible) over-parameterization/redundancy is given if there are (approximate) common zeros.

To evaluate parameter redundancy, the inverse roots of the AR and MA polynomials are examined for closeness with redtol determining closeness; see the note.

For fun, and IF the model is causal and invertible, setting plot.it=TRUE will display the complex plane with the inverse roots of the AR and MA polynomials displayed with colored arrows; the seasonal components are not included because it's too messy. The tolerance level for declaring over-parameterization is also displayed in the graphic.

Value

See the details. If the model is causal and invertible and not over-parameterized, a nice message of validation is given. Otherwise, problems are reported but the specific culprits may not be specified.

Note

The Fisher Information matrix for ARMA is singular for exact redundancy, and its closeness to singularity can be measured by the closeness of the inverse of those roots [e.g., Klein and Spreij (1997). On Fisher's information matrix of an ARMA process. In Stochastic Differential and Difference Equations, 273-284. Boston: Birkhauser.]

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

arma.spec, sarima.sim, ARMAtoAR, ARMAtoMA

Examples

arma.check(ar=c(1,-.9), sar=-.6, sma=-.4, S=4)

arma.check(ar=.9, ma=c(-.9,-.8), sar=1, S=12)

# hard to tell from parameters alone ...
arma.check(ar=c(1.5,-.75), ma=c(-.6,-.3,.45), plot.it=TRUE, gg=TRUE)

Description

Gives the ARMA model spectrum, but first tests for causality and invertibility, and then for parameter redundancy.

Usage

arma.spec(ar = 0, ma = 0, var.noise = 1, n.freq = 500, main = NULL, redundancy.tol=.1,
            frequency = 1, ylim = NULL, plot = TRUE, ...)

Arguments

Details

The basic call is arma.spec(ar, ma) where ar and ma are vectors containing the model parameters. Use log='y' if you want the plot on a log scale.

If the model is not causal or invertible, a stop error with a message is given; e.g., arma.spec(ar=1, ma=1) will just produce warnings.

If there are (approximate) common zeros, a spectrum will be displayed and a warning will be given; e.g., arma.spec(ar= .9, ma= -.9) will yield a warning and the plot will be the spectrum of white noise. See arma.check for details on the evaluation of parameter redundancy.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

arma.check

Examples

arma.spec(ar = c(1, -.9), ma = .8)

arma.spec(ar = c(1, -.9), log='y')

arma.spec(ar = -.9, ma=.89, gg=TRUE)  # almost white noise

# if you want a seasonal model, you have to be a little clever
arma.spec(ar=c(rep(0,11),.4), ma=.5, col=5, lwd=3, frequency=12)

Description

Gives the $\pi$-weights in the invertible representation of an ARMA model.

Usage

ARMAtoAR(ar = 0, ma = 0, lag.max=20)

Arguments

Value

A vector of coefficients. For an ARMA model $\phi(B) x_t = \theta(B) w_t$, returns the coefficients $\{\pi_j; \, j=1, 2, ...\}$ in the invertible representation $w_t = \pi(B) x_t = \sum_{j=0}^\infty \pi_j x_{t-j}$ where $\pi_0=1$.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

ARMAtoAR(ar=.9, ma=.5, 10)

Description

The script does one of two things. [1] Easily modify the opacity level of the astsa colors. [2] Create a color wheel of a chosen number of colors from a base color.

Usage

astsa.col(col=1, alpha=1, wheel=FALSE, pie=FALSE, num, sat=NULL, val=NULL, ...)

Arguments

Details

The astsa color palette is attached when the package is attached. The colors follow the R pattern of shades of: (1) black, (2) red, (3) green, (4) blue, (5) cyan, (6) magenta, (7) gold, (8) gray. The opacity of these colors can be changed easily using this script. Values are recycled, e.g., col=9 is the same as col=1.

Additionally, a color wheel can be generated by specifying a base color and inputting the number of desired colors. Using hsv, the script moves the 'hue' around the circle in equal steps holding 'saturation' and 'value' constant. This may be overridden by entering an alternate 'saturation' or 'value'.

In either application, a pie chart can be displayed to help in choosing the desired color scheme.

Value

[1] a color vector using the astsa color palette at the chosen transparency level
- OR -
[2] a color wheel of a chosen number num of colors from a base color

Author(s)

D.S.Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# View the astsa palette
astsa.col(1:8, pie=TRUE)
legend('topright', legend=astsa.col(1:8), fill=1:8, title='Hex Color Code')

# Plotting 2 series that touch (but in a nice way)
tsplot(cbind(gtemp_land, gtemp_ocean), col=astsa.col(c(4,2), .5), lwd=2, spaghetti=TRUE, 
     type='o', pch=20, ylab="Temperature Deviations", addLegend=TRUE, location='topleft',
     legend=c("Land Only", "Ocean Only"), gg=TRUE)  

# The hsv values for Dodgerblue3 (or astsa color 4)?
rgb2hsv(col2rgb(4))


# Wheels of fortune
vanna = par(no.readonly = TRUE)
par(mar=rep(0, 4))
layout( matrix(c(1,3,2,3), 2) )
astsa.col(4, wheel=TRUE, num=8, pie=TRUE)
astsa.col(4, wheel=TRUE, num=8, pie=TRUE, sat=.6, val=.9)
astsa.col(2, wheel=TRUE, num=100, pie=TRUE, border=FALSE, labels=NA)


# I'd like to solve the puzzle
par(vanna)  # reset graphic device
x = replicate(6, sarima.sim(ar=c(1.5,-.75), n=120))
tsplot(x, spag=TRUE, col=astsa.col(4, alpha=.7, wheel=TRUE, num=6), lwd=12)

Description

Uses minimum description length (MDL) to fit piecewise AR processes with the goal of detecting changepoints in time series. Optimization is accomplished via a genetic algorithm (GA).

Usage

autoParm(xdata, Pi.B = NULL, Pi.C = NULL, PopSize = 70, generation = 70, P0 = 20, 
         Pi.P = 0.3, Pi.N = 0.3, NI = 7)

Arguments

Details

Details my be found in Davis, Lee, & Rodriguez-Yam (2006). Structural break estimation for nonstationary time series models. JASA, 101, 223-239. doi:10.1198/016214505000000745

Value

Returns three values, (1) the breakpoints including the endpoints, (2) the number of segments, and (3) the segment AR orders. See the examples.

Note

The GA is a stochastic optimization procedure and consequently will give different results at each run. It is a good idea to run the algorithm a few times before coming to a final decision.

Author(s)

D.S. Stoffer

Source

The code is adapted from R code provided to us by Rex Cheung (https://www.linkedin.com/in/rexcheung).

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

autoSpec

Examples

## Not run: 

##-- simulation
x1 = sarima.sim(ar=c(1.69, -.81), n=500)
x2 = sarima.sim(ar=c(1.32, -.81), n=500) 
x = c(x1, x2)

##-- look at the data
tsplot(x)

##-- run procedure
autoParm(x)

##-- output (yours will be slightly different - 
##--         the nature of GA) 
# returned breakpoints include the endpoints 
# $breakpoints
# [1]    1  514 1000
# 
# $number_of_segments
# [1] 2
# 
# $segment_AR_orders
# [1] 2 2

## End(Not run)

Description

Uses changepoint detection to discover if there have been slight changes in frequency in a time series. The autoSpec procedure uses minimum description length (MDL) to do nonparametric spectral estimation with the goal of detecting changepoints. Optimization is accomplished via a genetic algorithm (GA).

Usage

autoSpec(xdata, Pi.B = NULL, Pi.C = NULL, PopSize = 70, generation = 70, m0 = 10, 
         Pi.P = 0.3, Pi.N = 0.3, NI = 7, taper = .5, min.freq = 0, max.freq = .5)

Arguments

Details

Details my be found in Stoffer, D. S. (2023). AutoSpec: Detection of narrowband frequency changes in time series. Statistics and Its Interface, 16(1), 97-108. doi:10.4310/21-SII703

Value

Returns three values, (1) the breakpoints including the endpoints, (2) the number of segments, and (3) the segment kernel orders. See the examples.

Note

The GA is a stochastic optimization procedure and consequently will give different results at each run. It is a good idea to run the algorithm a few times before coming to a final decision.

Author(s)

D.S. Stoffer

Source

The genetic algorithm code is adapted from R code provided to us by Rex Cheung (https://www.linkedin.com/in/rexcheung). The code originally supported Aue, Cheung, Lee, & Zhong (2014). Segmented model selection in quantile regression using the minimum description length principle. JASA, 109, 1241-1256. A similar version also supported Davis, Lee, & Rodriguez-Yam (2006). Structural break estimation for nonstationary time series models. JASA, 101, 223-239.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

autoParm

Examples

## Not run: 

##-- simulation
set.seed(1)
num = 500
t   = 1:num
w   = 2*pi/25
d   = 2*pi/150
x1  = 2*cos(w*t)*cos(d*t) + rnorm(num)
x2  = cos(w*t) + rnorm(num)
x   = c(x1,x2)

##-- plot and periodogram (all action below 0.1)
tsplot(x, main='not easy to see the change')
mvspec(x) 

##-- run procedure
autoSpec(x, max.freq=.1)

##-- output (yours will be slightly different - 
##--         the nature of GA) 
# returned breakpoints include the endpoints 
# $breakpoints
# [1]    1  503 1000
# 
# $number_of_segments
# [1] 2
# 
# $segment_kernel_orders_m
# [1] 2 4


##-- plot everything
par(mfrow=c(3,1))
tsplot(x, col=4)
 abline(v=503, col=6, lty=2, lwd=2)
mvspec(x[1:502],    kernel=bart(2), taper=.5, main='segment 1', col=4, xlim=c(0,.25))
mvspec(x[503:1000], kernel=bart(4), taper=.5, main='segment 2', col=4, xlim=c(0,.25))   

## End(Not run)

Description

Smoothing (triangular) kernel that decreases one unit from the center.

Usage

bart(m)

Arguments

Details

Uses kernel from the stats package to construct a Bartlett (triangular) kernel of width 2m + 1; see help(kernel) for further details.

Value

Returns an object of class tskernel with the coefficients, the kernel dimension, and attribute "Bartlett".

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

bart(4)                         # for a list
plot(bart(4), ylim=c(.01,.21))  # for a graph

Description

Daily returns of three banks, 1. Bank of America [boa], 2. Citibank [citi], and 3. JP Morgan Chase [jpm], from 2005 to 2017.

Format

The format is: Time-Series [1:3243, 1:3] from 2005 to 2017: -0.01378 -0.01157 -0.00155 -0.01084 0.01252 ... with column names "boa" "citi" "jpm" .

Source

Gong & Stoffer (2021). A Note on Efficient Fitting of Stochastic Volatility Models. Journal of Time Series Analysis, 42(2), 186-200.

https://github.com/nickpoison/Stochastic-Volatility-Models

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(BCJ, col=2:4)

Description

Infrasonic signal from a nuclear explosion.

Usage

data(beamd)

Format

A data frame with 2048 observations (rows) on 3 numeric variables (columns): sensor1, sensor2, sensor3.

Details

This is a data frame consisting of three columns (that are not time series objects). The data are an infrasonic signal from a nuclear explosion observed at sensors on a triangular array.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Monthly live births (adjusted) in thousands for the United States, 1948-1979.

Format

The format is: Time-Series [1:373] from 1948 to 1979: 295 286 300 278 272 268 308 321 313 308 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Multiple time series of measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is NA.

Format

Time-Series [1:91, 1:3] from 1 to 91: 2.33 1.89 2.08 1.82 1.82 ...

..$ : NULL ..$ : chr [1:3] "WBC" "PLT" "HCT"

Details

This data set is used in Chapter 6 for a missing data example.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

HCT, PLT, WBC

Examples

# use type='o' when plotting series with missing data
tsplot(blood, type='o', pch=19, cex=1.1, col=2:4, gg=TRUE, xlab='day')

Description

Nucleotide sequence of the BNRF1 gene of the Epstein-Barr virus (EBV): 1=A, 2=C, 3=G, 4=T. The data are used in Chapter 7.

Format

The format is: Time-Series [1:3954] from 1 to 3954: 1 4 3 3 1 1 3 1 3 1 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

head(bnrf1ebv)
head(dna2vector(bnrf1ebv))

Description

Nucleotide sequence of the BNRF1 gene of the herpesvirus saimiri (HVS): 1=A, 2=C, 3=G, 4=T. The data are used in Chapter 7.

Format

The format is: Time-Series [1:3741] from 1 to 3741: 1 4 3 2 4 4 3 4 4 4 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

head(bnrf1hvs)
head(dna2vector(bnrf1hvs))

Description

Monthly mean carbon dioxide (in ppm) measured at Mauna Loa Observatory, Hawaii. This is an update to co2 in the datasets package.

Format

The format is: Time-Series [1:781] from 1958 to 2023: 316 317 318 317 316 ...

Details

The carbon dioxide data measured as the mole fraction in dry air, on Mauna Loa constitute the longest record of direct measurements of CO2 in the atmosphere. They were started by C. David Keeling of the Scripps Institution of Oceanography in March of 1958 at a facility of the National Oceanic and Atmospheric Administration. NOAA started its own CO2 measurements in May of 1974, and they have run in parallel with those made by Scripps since then. Data are reported as a dry mole fraction defined as the number of molecules of carbon dioxide divided by the number of molecules of dry air multiplied by one million (ppm).

Due to the eruption of the Mauna Loa Volcano, measurements from Mauna Loa Observatory were suspended as of Nov. 29, 2022. Observations starting in December 2022 are from a site at the Maunakea Observatories, approximately 21 miles north of the Mauna Loa Observatory.

Note

The reason this data file is called cardox is because R has two datasets called CO2 and co2, which doesn't leave many options if you don't want to create potential problems like the dplyr people. Anyway, cardox sounds like the name of a cool character in some SciFi movie.

Source

https://gml.noaa.gov/ccgg/trends/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Calculates and plots the sample CCF of two time series.

Usage

ccf2(x, y, max.lag = NULL, main = NULL, ylab = "CCF", plot = TRUE,
         na.action = na.pass, type = c("correlation", "covariance"), ...)

Arguments

Details

This will produce a graphic of the sample corr[x(t+lag), y(t)] from -max.lag to max.lag. Also, the (rounded) values of the CCF are returned invisibly unless plot=FALSE. Similar details apply to the cross-covariance.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

pre.white, acf1, acf2, acfm

Examples

ccf2(soi, rec, plot=FALSE, max.lag=6)  # now you see it
ccf2(soi, rec)                          # now you don't

# happy birthday
ccf2(soi, rec, col=astsa.col(4, wheel=TRUE, num=6), lwd=4, gg=TRUE)

Description

Poultry (chicken), Whole bird spot price, Georgia docks, US cents per pound

Format

The format is: Time-Series [1:180] from August 2001 to July 2016: 65.6 66.5 65.7 64.3 63.2 ...

Source

https://www.indexmundi.com/commodities/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Lake Shasta inflow data. This is a data frame.

Format

A data frame with 454 observations (rows) on the following 6 numeric variables (columns): Temp, DewPt, CldCvr, WndSpd, Precip, Inflow.

Details

The data are 454 months of measured values for the climatic variables: air temperature, dew point, cloud cover, wind speed, precipitation, and inflow, at Lake Shasta, California.

Lake Shasta is a man-made reservoir that is situated on ancestral lands of the Shasta Indian Nation. The area around the lake was once a thriving homeland for the Shasta. The construction of the reservoir submerged many of these significant cultural sites, leading to displacement and hardship for the Shasta people. The California Gold Rush drew in outsiders in the late 1840s. For the Shasta, this was a devastating process as thousands of miners who did not respect the Shasta or their homeland, operated along various waterways. Introduction of diseases and fighting against white people, rapidly reduced the number of Shasta. For more information, see https://www.legendsofamerica.com/shasta-indians.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(climhyd, ncolm=2, col=2:7, lwd=2, scale=.9)

Description

Average weekly cardiovascular mortality in Los Angeles County; 508 six-day smoothed averages obtained by filtering daily values over the 10 year period 1970-1979.

Format

The format is: Time-Series [1:508] from 1970 to 1980: 97.8 104.6 94.4 98 95.8 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap, lap.xts

Description

Median annual cost per gigabyte (GB) of storage.

Format

The format is: Time-Series [1:29] from 1980 to 2008: 213000.00 295000.00 260000.00 175000.00 160000.00 ...

Note

This is a good data set for a first exercise on regression with autocorrelated errors.

Source

The data are retail prices per GB taken from a sample of manufacturers listed at https://mkomo.com/cost-per-gigabyte. From there, the median cost per GB was computed by year.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Returns a time series with the trend removed. The trend can be estimated using polynomial regression or using a lowess fit.

Usage

detrend(series, order = 1, lowess = FALSE, lowspan = 2/3)

Arguments

Value

The detrended series is returned.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

trend

Examples

tsplot( cbind(salmon, detrend(salmon)), gg=TRUE, main='Norwegian Salmon USD/KG' )

Description

Daily DJIA values from April 2006 - April 2016

Format

The format is: xts [1:2518, 1:5] 11279 11343 11347 11337 11283 ...
- attr(*, "class")= chr [1:2] "xts" "zoo"
..$ : chr [1:5] "Open" "High" "Low" "Close" "Volume"

Source

The data were obtained via the TTR package and Yahoo financial data. Unfortunately, this does not work now. It seems like the R package quantmod is a good bet and Yahoo still has financial data.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# the file is an 'xts' data file
# if 'xts' is not installed you can still do this

tsplot(djia, ncolm=2, col=2:6)               # no dates
tsplot(timex(djia), djia, ncolm=2, col=2:6)  # dates 

# differencing (on its own) loses an obs 
return = diff(log(djia[,'Close']))
tsplot(timex(djia)[-1], return, col=4, gg=TRUE, main='DJIA')

Description

Takes a string (e.g., a DNA sequence) of general form (e.g., FASTA) and converts it to a sequence of indicator vectors for use with the Spectral Envelope (specenv).

Usage

dna2vector(data, alphabet = NULL)

Arguments

Details

Takes a string of categories and converts it to a matrix of indicators. The data can then be used by the script specenv, which calculates the Spectral Envelope of the sequence (or subsequence). Many different type of sequences can be used, including FASTA and GenBank, as long as the data is a string of categories.

The indicator vectors (as a matrix) are returned invisibly in case the user forgets to put the results in an object wherein the screen would scroll displaying the entire sequence. In other words, the user should do something like xdata = dna2vector(data) where data is the original sequence.

If the DNA sequence is in a FASTA file, say sequence.fasta, the following code can be used to read the data into the session, create the indicator sequence and save it as a compressed R data file:

  fileName <- 'sequence.fasta'      # name of FASTA file
  data     <- readChar(fileName, file.info(fileName)$size)  # input the sequence
  myseq    <- dna2vector(data)      # convert it to indicators

  ##== to compress and save the data ==##
  save(myseq, file='myseq.rda')
  ##== and then load it when needed ==##
  load('myseq.rda')

Value

matrix of indicator vectors; returned invisibly

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

specenv

Examples

# Epstein-Barr virus (entire sequence included in astsa)
substr(EBV, start=1, stop=25)
xdata = dna2vector(EBV)
head(xdata)

# part of EBV with  1, 2, 3, 4 for "A", "C", "G", "T"
xdata = dna2vector(bnrf1ebv)
head(xdata)

# raw GenBank sequence
data <-
c("1 agaattcgtc ttgctctatt cacccttact tttcttcttg cccgttctct ttcttagtat
  61 gaatccagta tgcctgcctg taattgttgc gccctacctc ttttggctgg cggctattgc")
xdata = dna2vector(data, alphabet=c('a', 'c', 'g', 't'))
head(xdata)

# raw FASTA sequence
data <-
 c("AGAATTCGTCTTGCTCTATTCACCCTTACTTTTCTTCTTGCCCGTTCTCTTTCTTAGTATGAATCCAGTA
    TGCCTGCCTGTAATTGTTGCGCCCTACCTCTTTTGGCTGGCGGCTATTGCCGCCTCGTGTTTCACGGCCT")
xdata = dna2vector(data)
head(xdata)

Description

EBV nucleotide sequence - 172281 bp as a single string

Format

The format is: chr "AGAATTCGTCTT ..."

Note

EBV is not useful on its own, but using 'dna2vector', different regions can be explored. For example, ebv = dna2vector(EBV)

Source

https://www.ncbi.nlm.nih.gov/nuccore/V01555.2

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

dna2vector

Examples

substr(EBV, start=1, stop=25)
head(dna2vector(EBV))

Description

Multiple time series of quarterly U.S. unemployment, GNP, consumption, and government and private investment, from 1948-III to 1988-II.

Format

Multiple time series with 161 observations (rows) on the following 5 numeric variables (columns): unemp, gnp, consum, govinv, prinv.

Note

unemp is in percentage (of the labor force), and the others are in 1982 Billions USD.

Source

Young, P.C. and Pedregal, D.J. (1999). Macro-economic relativity: government spending, private investment and unemployment in the USA 1948-1998. Structural Change and Economic Dynamics, 10, 359-380.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(econ5, ncolm=2, col=2:6, lwd=2, title=colnames(econ5), 
         ylab=c('%', rep('Billions-USD', 4)))

Description

Estimation of the parameters in general linear state space models via the EM algorithm. Missing data may be entered as NA or as zero (0), however, use NAs if zero (0) can be an observation. Inputs in both the state and observation equations are allowed. This script replaces EM0 and EM1.

Usage

EM(y, A, mu0, Sigma0, Phi, Q, R, Ups = NULL, Gam = NULL, input = NULL, 
    max.iter = 100, tol = 1e-04)

Arguments

Details

This script replaces EM0 and EM1 by combining all cases and allowing inputs in the state and observation equations. It uses version 1 of the new Ksmooth script (hence correlated errors is not allowed).

The states $x_t$ are p-dimensional, the data $y_t$ are q-dimensional, and the inputs $u_t$ are r-dimensional for $t=1, \dots, n$. The initial state is $x_0 \sim N(\mu_0, \Sigma_0)$.

The general model is

$x_t = \Phi x_{t-1} + \Upsilon u_{t} + w_t \quad w_t \sim iid\ N(0, Q)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + v_t \quad v_t \sim iid\ N(0, R)$

where $w_t \perp v_t$. The observation noise covariance matrix is assumed to be diagonal and it is forced to diagonal otherwise.

The measurement matrices $A_t$ can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate $q \times p$ dimension.

Value

Note

The script does not allow for constrained estimation directly, however, constrained estimation is possible with some extra manipulations. There is an example of constrained estimation using EM at FUN WITH ASTSA, where the fun never stops.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Kfilter, Ksmooth

Examples

y = ar1miss   # an 'astsa' data set with missing values
A = 1; Phi = .1; Ups = 1
Q = 0.1; R = 0.1; Gam=1
mu0 = 0; Sigma0 = 1
input = rep(1, length(y))
( em = EM(y, A, mu0, Sigma0, Phi, Q, R, Ups, Gam, input) ) 

# run Kalman smoother at the final estimates
ks = Ksmooth(y, A=1, em$mu0, em$Sigma0, em$Phi, sQ=sqrt(em$Q), sR=sqrt(em$R),
              Ups=em$Ups, Gam=em$Gam, input=input) 

# admire your work
tsplot(cbind(y, drop(ks$Xs)), type='o', pch=c(19,NA), col=2*2:3, lwd=1:2, 
        gg=TRUE, spag=TRUE, addLegend=TRUE, legend=c('data', 'smooth'))
miss = cbind(which(is.na(y)), min(y, na.rm=TRUE)-.2)   # show yourself
points(miss, pch=18)

Description

Southern Oscillation Index (SOI), 1/1951 to 10/2022; anomalies are departures from the 1981-2010 base period.

Format

The format is: Time-Series [1:862] from 1951 to 2022: 2.0 1.1 -0.3 -0.8 -1.1 -0.7 -1.5 -0.3 -0.7 -0.7 ...

Details

The $\textrm{El Ni\~no - Southern Oscillation (ENSO)}$ is a recurring climate pattern involving changes in the temperature of waters in the central and eastern tropical Pacific Ocean. This data set is an update to soi.

Source

https://www.ncei.noaa.gov/access/monitoring/enso/soi

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

soi, ENSO, MEI, MEI2

Examples

# ENSO is a standardized index based on the sea level pressure differences between 
# Tahiti and Darwin, Australia.  MEI is a similar index based on multiple factors.
# As opposed to ENSO (and SOI), positive values of MEI correspond to warmer temperatures.

tsplot(cbind(-ENSO, MEI), col=astsa.col(2*2:1, .6), addLegend=TRUE, spag=TRUE, lwd=1:2)

tspairs(ts.intersect(-ENSO, MEI), location='top')

Description

Seismic trace of an earthquake [two phases or arrivals along the surface, the primary wave ($t = 1,\dots,1024$) and the shear wave ($t = 1025,\dots,2048$)] recorded at a seismic station.

Format

The format is: Time-Series [1:2048] from 1 to 2048: 0.01749 0.01139 0.01512 0.01477 0.00651 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

eqexp

Description

Series of annual counts of major earthquakes (magnitude 7 and above) in the world between 1900 and 2006.

Format

The format is: Time-Series [1:107] from 1900 to 2006: 13 14 8 10 16 26 ...

Source

Zucchini and MacDonald (2009). Hidden Markov Models for Time Series: An Introduction using R. CRC Press.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

This is a data frame of the earthquake and explosion seismic series used throughout the text.

Format

A data frame with 2048 observations (rows) on 17 variables (columns). Each column is a numeric vector.

Details

The matrix has 17 columns, the first eight are earthquakes, the second eight are explosions, and the last column is the Novaya Zemlya event of unknown origin.

The column names are: EQ1, EQ2,...,EQ8; EX1, EX2,...,EX8; NZ. The first 1024 observations correspond to the P wave, the second 1024 observations correspond to the S wave.

All events in the data set were on or near land and were distributed uniformly over Scandinavia so as to minimize the possibility that discriminators might be keying on location or land-sea differences. The events are earthquakes ranging in magnitude from 2.74 to 4.40 and explosions in the range 2.13 to 2.19. Also added is an event of uncertain origin that was located in the Novaya Zemlya region of Russia. All events except the Russian event occurred in the Scandinavian peninsula and were recorded by seismic arrays located in Norway by Norwegian and Arctic experimental seismic stations (NORESS, ARCESS) and in Finland by Finnish experimental seismic stations (FINESS).

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# view all series 
# first 2 rows EQs - next 2 rows EXs
# 5th row NZ event 

tsplot(eqexp, ncol=4, col=c(rep(6,8),rep(4,8),2), scale=.75)

## Not run: 

# for a nice html map, use the 'leaflet' package

library(leaflet)   # install if you don't have it

lat = c(
65.5,65.7,64.5,67.8,59.2,51.4,59.5,66.9,
69.2,61.8,67.6,67.6,67.1,59.5,69.4,64.7,
73.6)

long = c(
22.9,32.1,21.3,15.1,10.9,6.1,5.9,13.7,
34.3,30.7,33.9,30.6,21.0,24.1,30.8,30.8,
55.2)

event = c(
"EQ1","EQ2","EQ3","EQ4","EQ5","EQ6","EQ7","EQ8",
"EX1","EX2","EX3","EX4","EX5","EX6","EX7","EX8",
"NZ")


eventmap = data.frame(
  longitude = long,
  latitude = lat,
  event = event )

leaflet(eventmap) %>%
  addTiles() %>% 
  addMarkers(~longitude, ~latitude, label = ~event,
    labelOptions = labelOptions(noHide = TRUE))


## End(Not run)

Description

Estimates the ESS of a given vector of samples.

Usage

ESS(trace, tol = 1e-08, BIC = TRUE, digits=2)

Arguments

Details

Uses spec.ic to estimate the spectrum of the input at frequency zero (spec0). Then, ESS is estimated as ESS = length(trace)*var(trace)/spec0. See Examples for multivariate case.

ESS is discussed in detail in Example 6.31 of Time Series Analysis and Its Applications: With R Examples (5th ed, 2025).

Value

Returns the estimated ESS of the input.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# How autocorrelation affects ESS
# get a few Markov chains
x   = matrix(NA, 500, 3)  # sample size is 500
phi = c(0,.3,.9)          # no, low, high
for (i in 1:3) x[,i] = sarima.sim(ar=phi[i])
apply(x, 2, ESS, digits=0)

Description

Seismic trace of an explosion [two phases or arrivals along the surface, the primary wave ($t = 1,\dots,1024$) and the shear wave ($t = 1025,\dots,2048$)] recorded at a seismic station.

Format

The format is: Time-Series [1:2048] from 1 to 2048: -0.001837 -0.000554 -0.002284 -0.000303 -0.000721 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

eqexp

Description

Computes the basic false discovery rate given a vector of p-values and returns the index of the maximal p-value satisfying the FDR condition.

Usage

FDR(pvals, qlevel = 0.05)

Arguments

Value

Note

This is used primarily in Chapter 7.

Source

Built off of https://www.stat.berkeley.edu/~paciorek/code/fdr/fdr.R.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

FFBS algorithm for state space models

Usage

ffbs(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, input = NULL)

Arguments

Details

For a linear state space model, the FFBS algorithm provides a way to sample a state sequence $x_{0:n}$ from the posterior $\pi(x_{0:n} \mid \Theta, y_{1:n})$ with parameters $\Theta$ and data $y_{1:n}$.

The general model is

$x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)$

where $w_t \perp v_t$. Consequently the state noise covariance matrix is $Q = sQ\, sQ'$ and the observation noise covariance matrix is $R = sR\, sR'$ and $sQ, sR$ do not have to be square as long as everything is conformable.

$x_t$ is p-dimensional, $y_t$ is q-dimensional, and $u_t$ is r-dimensional. Note that $sQ\, w_t$ has to be p-dimensional, but $w_t$ does not, and $sR\, v_t$ has to be q-dimensional, but $v_t$ does not.

Value

Note

The script uses Kfilter. If $A_t$ is constant wrt time, it is not necessary to input an array; see the example. The example below is just one pass of the algorithm; see the example at FUN WITH ASTSA for the real fun.

Author(s)

D.S. Stoffer

Source

Chapter 6 of the Shumway and Stoffer Springer text.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

## -- this is just one pass --##
# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }

## run one pass of FFBS, plot data, states and sampled states  
run = ffbs(y, A=1, mu0=0, Sigma0=10, Phi=1, sQ=1, sR=3)
tsplot(cbind(y,run$Xs), spaghetti=TRUE, type='o', col=c(8,4), pch=c(1,NA))
legend('topleft', legend=c("y(t)","xs(t)"), lty=1, col=c(8,4), bty="n", pch=c(1,NA))

## End(Not run)

Description

Monthly pneumonia and influenza deaths per 10,000 people in the United States for 11 years, 1968 to 1978.

Usage

data(flu)

Format

The format is: Time-Series [1:132] from 1968 to 1979: 0.811 0.446 0.342 0.277 0.248 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Data (as a vector list) from an fMRI experiment in pain, listed by location and stimulus. The data are BOLD signals when a stimulus was applied for 32 seconds and then stopped for 32 seconds. The signal period is 64 seconds and the sampling rate was one observation every 2 seconds for 256 seconds ($n = 128$). The number of subjects under each condition varies.

Details

The LOCATIONS of the brain where the signal was measured were [1] Cortex 1: Primary Somatosensory, Contralateral, [2] Cortex 2: Primary Somatosensory, Ipsilateral, [3] Cortex 3: Secondary Somatosensory, Contralateral, [4] Cortex 4: Secondary Somatosensory, Ipsilateral, [5] Caudate, [6] Thalamus 1: Contralateral, [7] Thalamus 2: Ipsilateral, [8] Cerebellum 1: Contralateral and [9] Cerebellum 2: Ipsilateral.

The TREATMENTS or stimuli (and number of subjects in each condition) are [1] Awake-Brush (5 subjects), [2] Awake-Heat (4 subjects), [3] Awake-Shock (5 subjects), [4] Low-Brush (3 subjects), [5] Low-Heat (5 subjects), and [6] Low-Shock (4 subjects). Issue the command summary(fmri) for further details. In particular, awake (Awake) or mildly anesthetized (Low) subjects were subjected levels of periodic brushing (Brush), application of heat (Heat), and mild shock (Shock) effects.

As an example, fmri$L1T6 (Location 1, Treatment 6) will show the data for the four subjects receiving the Low-Shock treatment at the Cortex 1 location; note that fmri[[6]] will display the same data.

Source

Joseph F. Antognini, Michael H. Buonocore, Elizabeth A. Disbrow, Earl Carstens, Isoflurane anesthesia blunts cerebral responses to noxious and innocuous stimuli: a fMRI study, Life Sciences, Volume 61, Issue 24, 1997, Pages PL349-PL354, ISSN 0024-3205,
https://doi.org/10.1016/S0024-3205(97)00960-0.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

A data frame that consists of average fMRI BOLD signals at eight locations.

Usage

data(fmri1)

Format

The format is: mts [1:128, 1:9]

Details

Multiple time series consisting of fMRI BOLD signals at eight locations (in columns 2-9, column 1 is time period), when a stimulus was applied for 32 seconds and then stopped for 32 seconds. The signal period is 64 seconds and the sampling rate was one observation every 2 seconds for 256 seconds ($n = 128$). The columns are labeled: "time" "cort1" "cort2" "cort3" "cort4" "thal1" "thal2" "cere1" "cere2".

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

fmri

Examples

tsplot(fmri1[,2:9], ncolm=4, gg=TRUE, col=c(rep(4,4),rep(3,2),rep(6,2)))

Description

New York Harbor conventional regular gasoline weekly spot price FOB (in cents per gallon) from 2000 to mid-2010.

Format

The format is: Time-Series [1:545] from 2000 to 2010: 70.6 71 68.5 65.1 67.9 ...

Details

Pairs with series oil

Source

Data were obtained from: https://www.eia.gov/dnav/pet/pet_pri_spt_s1_w.htm

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

oil

Examples

tsplot(cbind(gas,oil), spag=TRUE, col=2*1:2, addLegend=TRUE)

Description

Seasonally adjusted quarterly U.S. GDP from 1947(1) to 2018(3).

Format

The format is: Time-Series [1:287] from 1947 to 2018: 2033 2028 2023 2055 2086 ...

Source

https://tradingeconomics.com/united-states/gdp

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

GDP, GNP, gnp

Description

Seasonally adjusted quarterly U.S. GDP from 1947(1) to 2023(1).

Format

The format is: Time-Series [1:305] from 1947 to 2023: 243.164 245.968 249.585 259.745 ...

Source

https://fred.stlouisfed.org/series/GDP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gdp, GNP, gnp

Description

Seasonally adjusted quarterly U.S. GNP from 1947(1) to 2002(3).

Format

The format is: Time-Series [1:223] from 1947 to 2002: 1489 1497 1500 1524 1547 ...

Source

https://fred.stlouisfed.org/series/GNP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

GNP, GDP, gdp

Description

Seasonally adjusted quarterly U.S. GNP from 1947(1) to 2003(1).

Format

The format is: Time-Series [1:305] from 1947 to 2023: 244.142 247.063 250.716 260.981 ...

Source

https://fred.stlouisfed.org/series/GNP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gnp, GDP, gdp

Description

Adds a grid to an existing plot with major and minor ticks. Works like R graphics grid() but the grid lines are solid and gray and minor ticks are produced by default.

Usage

Grid(nx = NULL, ny = nx, col = gray(0.9), lty = 1, lwd = par("lwd"), equilogs = TRUE,
    minor = TRUE, nxm = 2, nym = 2, tick.ratio = 0.5, xm.grid = TRUE, ym.grid = TRUE, ...)

Arguments

Author(s)

D.S. Stoffer

Source

The code for grid() in R 'graphics' and minor.tick() from the 'Hmisc' package were combined and then washed, polished, and coated with a subtle metallic finish. The grid now sparkles in the sunlight.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

grid

Description

Annual temperature anomalies (in degress centigrade) averaged over the Earth's land and ocean area from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.24 -0.25 -0.27 -0.15 -0.05 -0.16 -0.29 -0.32 -0.19 -0.04 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_land, gtemp_ocean

Description

Annual temperature anomalies (in degress centigrade) averaged over the Earth's land area from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.50 -0.60 -0.50 -0.50 -0.20 -0.50 -0.80 -0.40 -0.40 -0.10 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_ocean, gtemp_both

Description

Annual sea surface temperature anomalies averaged over the part of the ocean that is free of ice at all times (open ocean) from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.12 -0.08 -0.14 0.04 0.04 0.00 -0.05 -0.27 -0.09 0.01 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_land, gtemp_both

Description

Monthly global average surface temperatures by year. The temperature of the air measured 2 meters above the ground, encompassing land, sea, and in-land water surfaces.

Format

A data frame with 12 monthly observations (as rows) for the years 1975-2023 (as columns in reverse order).

Details

Temperature of air at 2m above the surface of land, sea or in-land waters. 2m temperature is calculated by interpolating between the lowest model level and the Earth's surface, taking account of the atmospheric conditions. Technical details at https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels-monthly-means?tab=overview.

Source

https://ourworldindata.org/grapher/monthly-average-surface-temperatures-by-year

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# functional data plot showing global warming
tsplot(gtemp.month, spaghetti=TRUE, col=rainbow(49, start=.2, v=.8, rev=TRUE), ylab='\u00b0C', 
        xlab='Month', xaxt='n', main='Mean Monthly Global Temperature', lwd=c(3,rep(1,47),3))
axis(1, labels=Months, at=1:12)
text(10, 13, '1975')
text(10.3, 15.5, '2023')

Description

This is one of the classic studies of predator-prey interactions, the 90-year data set is the number, in thousands, of snowshoe hare pelts purchased by the Hudson's Bay Company (HBC) of Canada. While this is an indirect measure of predation, the assumption is that there is a direct relationship between the number of pelts collected and the number of hare and lynx in the wild.

If you are interested in the brutal story of HBC, see the video https://www.nfb.ca/film/other_side_of_the_ledger or read the article https://canadiangeographic.ca/articles/the-untold-story-of-the-hudsons-bay-company.

Format

The format is: Time-Series [1:91] from 1845 to 1935: 19.6 19.6 19.6 12 28 ...

Note

This data set pairs with Lynx. The data are in units of one thousand.

Source

From Odum's "Fundamentals of Ecology", p. 191. Data listed at:
http://people.whitman.edu/~hundledr/courses/M250F03/M250.html
scroll down to: Chapter 6, Difference Equations.

NB: For some reason, there is not a secure and encrypted version of the site above.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Lynx

Description

HCT: Measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is 0 (zero).

Format

The format is: Time-Series [1:91] from 1 to 91: 30 30 28.5 34.5 34 32 30.5 31 33 34 ...

Details

See Examples 6.1 and 6.9 for more details.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

blood, PLT, WBC

Description

Quarterly Hawaiian hotel occupancy rate (percent of rooms occupied) from 1982-I to 2015-IV

Format

The format is: Time-Series [1:136] from 1982 to 2015: 79 65.9 70.9 66.7 ...

Source

https://dbedt.hawaii.gov/economic/qser/tourism/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(hor, type='c')                           # plot data and
text(hor, labels=1:4, col=c(1,4,2,6), cex=.9)   # add quarter labels

Description

Johnson and Johnson quarterly earnings per share, 84 quarters (21 years) measured from the first quarter of 1960 to the last quarter of 1980.

Format

The format is: Time-Series [1:84] from 1960 to 1981: 0.71 0.63 0.85 0.44 0.61 0.69 0.92 0.55 0.72 0.77 ...

Details

The data were provided (personal communication) by Professor Paul Griffin, https://gsm.ucdavis.edu/profile/paul-griffin, of the Graduate School of Management, University of California, Davis. This data set is also included with the R distribution as JohnsonJohnson.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Description

Returns both the predicted and filtered values for various linear state space models; it also evaluates the likelihood at the given parameter values.

Usage

Kfilter(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, 
         input = NULL, S = NULL, version = 1)

Arguments

Details

This script replaces Kfilter0, Kfilter1, and Kfilter2 by combining all cases. The major difference is how to specify the covariance matrices; in particular, sQ = t(cQ) and sR = t(cR) where cQ and cR were used in Kfilter0-1-2 scripts.

The states $x_t$ are p-dimensional, the data $y_t$ are q-dimensional, and the inputs $u_t$ are r-dimensional for $t=1, \dots, n$. The initial state is $x_0 \sim N(\mu_0, \Sigma_0)$.

The measurement matrices $A_t$ can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate $q \times p$ dimension.

Version 1 (default): The general model is

$x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)$

where $w_t \perp v_t$. Consequently the state noise covariance matrix is $Q = sQ\, sQ'$ and the observation noise covariance matrix is $R = sR\, sR'$ and $sQ, sR$ do not have to be square as long as everything is conformable. Notice the specification of the state and observation covariances has changed from the original scripts.

NOTE: If it is easier to model in terms of $Q$ and $R$, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Version 2 (correlated errors): The general model is

$x_{t+1} = \Phi x_{t} + \Upsilon u_{t+1} + sQ\, w_t \quad w_t \sim iid\ N(0,I)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)$

where $S = {\rm Cov}(w_t, v_t)$, and NOT ${\rm Cov}(sQ\, w_t, sR\, v_t)$.

NOTE: If it is easier to model in terms of $Q$ and $R$, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Note that in either version, $sQ\, w_t$ has to be p-dimensional, but $w_t$ does not, and $sR\, v_t$ has to be q-dimensional, but $v_t$ does not.

Value

Time varying values are returned as arrays.

Note

If it is easier to model in terms of $Q$ and $R$, simply input the square root matrices sQ = Q%^%.5 and sR = R%^%.5.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Ksmooth

Examples

# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }
# run and plot the filter  
run = Kfilter(y, A=1, mu0, Sigma0, Phi=1, sQ, sR)

tsplot(cbind(x, y, Xf=run$Xf), spaghetti=TRUE, type='o', col=c(3,4,6), pch=c(NA,1,NA),
       addLegend=TRUE, location='topleft', lwd=c(2,1,2))

Description

Returns the smoother values for various linear state space models. The predicted and filtered values and the likelihood at the given parameter values are also returned (via Kfilter).

Usage

Ksmooth(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, 
         input = NULL, S = NULL, version = 1)

Arguments

Details

The states $x_t$ are p-dimensional, the data $y_t$ are q-dimensional, and the inputs $u_t$ are r-dimensional for $t=1, \dots, n$. The initial state is $x_0 \sim N(\mu_0, \Sigma_0)$.

The measurement matrices $A_t$ can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate $q \times p$ dimension.

Version 1 (default): The general model is

$x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)$

where $w_t \perp v_t$. Consequently the state noise covariance matrix is $Q = sQ\, sQ'$ and the observation noise covariance matrix is $R = sR\, sR'$ and $sQ, sR$ do not have to be square as long as everything is conformable. Notice the specification of the state and observation covariances has changed from the original scripts.

NOTE: If it is easier to model in terms of $Q$ and $R$, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Version 2 (correlated errors): The general model is

$x_{t+1} = \Phi x_{t} + \Upsilon u_{t+1} + sQ\, w_t \quad w_t \sim iid\ N(0,I)$

$y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)$

where $S = {\rm Cov}(w_t, v_t)$, and NOT ${\rm Cov}(sQ\, w_t, sR\, v_t)$.

NOTE: If it is easier to model in terms of $Q$ and $R$, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Note that in either version, $sQ\, w_t$ has to be p-dimensional, but $w_t$ does not, and $sR\, v_t$ has to be q-dimensional, but $v_t$ does not.

Value

Time varying values are returned as arrays.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Kfilter

Examples

# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }

# run and plot the smoother  
run = Ksmooth(y, A=1, mu0, Sigma0, Phi=1, sQ, sR)

tsplot(cbind(x, y, Xs=run$Xs), spaghetti=TRUE, type='o', col=c(3,4,6), pch=c(NA,1,NA),
       addLegend=TRUE, location='topleft', lwd=c(2,1,2), gg=TRUE)