tvar {timsac}R Documentation

Time Varying Coefficients AR model

Description

Estimate time varying coefficients AR model.

Usage

  tvar(y, ar.order, trend.order=2, span, outlier, 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 value for computing variance of the system noise tau2.
delta delta for computing variance of the system noise tau2. If tau20 is NULL or delta is NULL, tau2 is computed automatically.
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) + ... + 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 zwro mean white noise.

Value

tau2 variance of the system noise.
sigma2 variance of the observational noise.
lkhood log-likelihood.
aic AIC.
arcoef time varying AR coefficients.
parcor partial autocorrelation coefficient.
spec time varying spectrum.

References

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

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 Controle, AC-30, 48-56.

Examples

  data(MYE1F) # an earthquake wave data
  z <- tvvar(MYE1F, trend.order=2, tau20= 6.6e-06, delta=1.0e-06, plot=FALSE)
  zz <- tvar(z$normdat, ar.order=4, trend.order=2, span=20, tau20=6.6e-06, delta=1.0e-06, outlier=c(630,1026))
  zz$tau2
  zz$sigma2
  zz$lkhood
  zz$aic

[Package timsac version 1.2.1 Index]