The TSMLOMAR subroutine analyzes nonstationary or locally stationary multivariate time series by using the minimum AIC procedure.

The input arguments to the TSMLOMAR subroutine are as follows:

data

specifies a data matrix, where is the number of observations and is the number of variables to be analyzed.

maxlag

specifies the maximum lag of the vector AR (VAR) process. This value should be less than of the length of locally stationary spans. The default is maxlag=10.

opt

specifies an options vector.

opt[1]

specifies the mean deletion option. The mean of the original data is deleted if opt[1]=. An intercept coefficient is estimated if opt[1]=1. If opt[1]=0, the original input data are processed assuming that the mean values of input series are zeros. The default is opt[1]=0.

opt[2]

specifies the span length to be used when breaking up the time series into separate blocks. By default, , which forces all of the time series values into a single span.

opt[3]

specifies the minimum AIC option. If opt[3]=0, the maximum lag VAR process is estimated. If opt[3]=1, a minimum AIC procedure is used. The default is opt[3]=1.

missing

specifies the missing value option. By default, only the first contiguous observations with no missing values are used (missing=0). The missing=1 option ignores observations with missing values. If you specify the missing=2 option, the missing values are replaced with the sample mean.

print

specifies the print option. By default, printed output is suppressed (print=0). The print=1 option prints the AR estimates, minimum AIC, minimum AIC order, and innovation variance matrix.

The TSMLOMAR subroutine returns the following values.

arcoef

refers to an VAR coefficient vector of the final model if the intercept vector is not included. If opt[1]=1, the first column of the arcoef matrix is an intercept estimate vector.

ev

refers to the error variance matrix.

nar

is the selected VAR order of the final model. If opt[3]=0, nar=maxlag.

aic

refers to the minimum AIC value of the final model.

start

refers to the starting position of the input series data, which corresponds to the first observation of the final model.

finish

refers to the ending position of the input series data, which corresponds to the last observation of the final model.

The TSMLOMAR subroutine analyzes nonstationary (or locally stationary) multivariate time series by using the minimum AIC procedure. The data of length is divided into locally stationary subseries. See "Nonstationary Time Series" in the section Nonstationary Time Series for details.