tvvar {TSSS} | R Documentation |
Time Varying Variance
Description
Estimate time-varying variance.
Usage
tvvar(y, trend.order, tau2.ini = NULL, delta, plot = TRUE, ...)
Arguments
y |
a univariate time series. |
trend.order |
trend order. |
tau2.ini |
initial estimate of variance of the system noise |
delta |
search width. |
plot |
logical. If |
... |
graphical arguments passed to the |
Details
Assuming that , we define a transformed time series
by
where is a Gaussian white noise with mean
and variance
.
is distributed as a
distribution with
degrees of freedom, so the probability density function of
is given by
By further transformation
the probability density function of is given by
Therefore, the transformed time series is given by
where is a double exponential distribution with probability density
function
In the space state model
by identifying trend components of , the log variance of original
time series
is obtained.
Value
An object of class "tvvar"
which has a plot
method. This is a
list with the following components:
tvv |
time varying variance. |
nordata |
normalized data. |
sm |
transformed data. |
trend |
trend. |
noise |
residuals. |
tau2 |
variance of the system noise. |
sigma2 |
variance of the observational noise. |
llkhood |
log-likelihood of the model. |
aic |
AIC. |
tsname |
the name of the univariate time series |
References
Kitagawa, G. (2020) Introduction to Time Series Modeling with Applications in R. 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.
Examples
# seismic data
data(MYE1F)
tvvar(MYE1F, trend.order = 2, tau2.ini = 6.6e-06, delta = 1.0e-06)