TSSS (version 1.2.3)

tvar: Time Varying Coefficients AR Model

Description

Estimate time varying coefficients AR model.

Usage

tvar(y, trend.order = 2, ar.order = 2, span, outlier = NULL, tau2.ini = NULL,
     delta, plot = TRUE)

Arguments

y

a univariate time series.

trend.order

trend order (1 or 2).

ar.order

AR order.

span

local stationary span.

outlier

positions of outliers.

tau2.ini

initial estimate of variance of the system noise \(\tau^2\). If tau2.ini = NULL, the most suitable value is chosen in \(\tau^2 = 2^{-k}\).

delta

search width.

plot

logical. If TRUE (default), 'parcor' is plotted.

Value

arcoef

time varying AR coefficients.

sigma2

variance of the observational noise \(\sigma^2\).

tau2

variance of the system noise \(\tau^2\).

llkhood

log-likelihood of the model.

aic

AIC.

parcor

partial autocorrelation coefficient.

Details

The time-varying coefficients AR model is given by

$$y_t = a_{1,t}y_{t-1} + \ldots + a_{p,t}y_{t-p} + u_t$$

where \(a_{i,t}\) is \(i\)-lag AR coefficient at time \(t\) and \(u_t\) is a zero mean white noise.

The time-varying spectrum can be plotted using AR coefficient arcoef and variance of the observational noise sigma2 by plot.tvspc (see tvspc).

References

Kitagawa, G. (2010) Introduction to Time Series Modeling. Chapman & Hall/CRC.

Kitagawa, G. and Gersch, W. (1996) Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics, No.116, Springer-Verlag.

Kitagawa, G. and Gersch, W. (1985) A smoothness priors time varying AR coefficient modeling of nonstationary time series. IEEE trans. on Automatic Control, AC-30, 48-56.

Examples

# NOT RUN {
# seismic data
data(MYE1F)
z <- tvar(MYE1F, trend.order = 2, ar.order = 8, span = 20,
          outlier = c(630, 1026), tau2.ini = 6.6e-06, delta = 1.0e-06)
z

spec <- tvspc(z$arcoef, z$sigma2)
plot(spec, theta = 30, phi = 40, expand = 0.5)
# }