timsac (version 1.2.7)

tvar: Time Varying Coefficients AR model

Description

Estimate time varying coefficients AR model.

Usage

tvar(y, ar.order, trend.order=2, span, outlier=NULL, tau20=NULL,
       delta=NULL, plot=TRUE)

Arguments

y

a univariate time series.

ar.order

AR order.

trend.order

trend order (1 or 2).

span

local stationary span.

outlier

positions of outliers.

tau20

initial estimate of variance of the system noise tau2.

delta

search width. If tau2 is NULL or delta is NULL, tau2 is computed automatically.

plot

logical. If TRUE (default) parcor is plotted.

Value

• tau2max
  variance of the system noise for maximum log-likelihood.
• sigma2
  variance of the observational noise.
• lkhood
  log-likelihood.
• aic
  AIC.
• arcoef
  time varying AR coefficients.
• 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.

References

Kitagawa, G. (1993) Time series analysis programing (in Japanese). The Iwanami Computer Science Series. 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

data(MYE1F) # an earthquake wave data
  z <- tvar(MYE1F, 4, 2, 20, c(630,1026), 6.6e-06, 1.0e-06)
  z$tau2max
  z$sigma2
  z$lkhood
  z$aic