The TSTVCAR subroutine analyzes time series that are nonstationary in the covariance function.

The input arguments to the TSTVCAR subroutine are as follows:

data

specifies a (or ) data vector.

nar

specifies the order of the AR process. The default is nar=8.

init

specifies the initial values of the parameter estimates. The default is (1E4, 0.3, 1E5, 0).

opt

specifies an options vector.

opt[1]

specifies the mean deletion option. The mean of the original series is subtracted from the series if opt[1]=. By default, the original series is processed (opt[1]=0).

opt[2]

specifies the filtering period (nfilter). The number of state vectors is determined by . The default is opt[2]=10.

opt[3]

specifies the numerical differentiation method. If opt[3]=1, the one-sided (forward) differencing method is used. The two-sided (or central) differencing method is used if opt[3]=2. The default is opt[3]=1.

outlier

specifies the vector of outlier observations. The value should be less than or equal to the maximum number of observations. The default is outlier=0.

print

specifies the print option. By default, printed output is suppressed (print=0). The print=1 option prints the final estimates. The iteration history is printed if print=2.

The TSTVCAR subroutine returns the following values:

arcoef

refers to the time-varying AR coefficients.

variance

refers to the time-varying error variances. See the section Smoothness Priors Modeling for details.

est

refers to the parameter estimates.

aic

refers to the value of AIC from the final estimates.

Nonstationary time series modeling usually deals with nonstationarity in the mean. The TSTVCAR subroutine analyzes the model that is nonstationary in the covariance. Smoothness priors are imposed on each time-varying AR coefficient and frequency response function. See the section Nonstationary Time Series for details.