tvvar {timsac}R Documentation

Time Varying Variance

Description

Estimate time-varying variance.

Usage

  tvvar(y, trend.order, tau20, delta, plot=TRUE)

Arguments

y univariate time series.
trend.order trend order.
tau20 initial estimate of tau2.
delta search width.
plot logical. If TRUE (default) normdat, ts, trend and noise are plotted.

Details

A chi-square distribution with digree 2 is given by

s(m) = y(2m-1)**2 + y(2m)**2

where y(n) is original scalar time series and σ(2m-1)**2 = σ(2m)**2.

z(m) = log(s(m)/2).

z(m) = log(σ**2) + w(m),

where w(m) is a double exponential distribution with density h(w) = exp{w-e**w}.

The space state model is given by

z(m) = t(m) + w(m).

Value

tvvar time varying variance.
normdat normalized data.
ts tranceformed time series s(m).
trend trend.
noise residuals.
tau2 variance of the system noise tau2.
sigma2 variance of the observational noise.
lkhood log-likelihood of the mode.
aic AIC.

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)
  z$lkhood
  z$aic

[Package timsac version 1.2.1 Index]