tvar {TSSS} | R Documentation |
Estimate time varying coefficients AR model.
tvar(y, trend.order = 2, ar.order = 2, span, outlier = NULL, tau2.ini = NULL, delta, plot = TRUE)
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 τ^2.
If |
delta |
search width. |
plot |
logical. If |
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 zero mean white noise.
The time-varying spectrum can be plotted using AR coefficient arcoef
and variance of the observational noise sigma2
by plot.tvspc
(see tvspc).
arcoef |
time varying AR coefficients. |
sigma2 |
variance of the observational noise σ^2. |
tau2 |
variance of the system noise τ^2. |
llkhood |
log-likelihood of the model. |
aic |
AIC. |
parcor |
partial autocorrelation coefficient. |
Kitagawa, G. (2010) Introduction to Time Series Modeling. 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.
# 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, theta = 30, phi = 40, expand = 0.5)