tvvar {timsac} | R Documentation |
Estimate time-varying variance.
tvvar(y, trend.order, tau20, delta, plot=TRUE)
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. |
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).
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. |
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.
data(MYE1F) # an earthquake wave data z <- tvvar(MYE1F, trend.order=2, tau20= 6.6e-06, delta=1.0e-06) z$lkhood z$aic