TSSS (version 1.3.4-5)

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)

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

PARCOR.

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.

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 tvspc.

References

Kitagawa, G. (2020) Introduction to Time Series Modeling with Applications in R. 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.

See Also

tvspc, plot.tvspc

Examples

# 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)