The TSMULMAR subroutine estimates VAR processes by using the minimum AIC procedure.

The input arguments to the TSMULMAR 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 VAR process. This value should be less than of the length of input data. 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 vector is estimated if opt[1]=1. If opt[1]=0, the original input data are processed assuming that the mean value of the input data is 0. The default is opt[1]=0.

opt[2]

specifies the minimum AIC option. If opt[2]=0, the maximum lag AR process is estimated. If opt[2]=1, the minimum AIC procedure is used, while the opt[2]=2 option specifies the VAR order selection method based on the AIC. The default is opt[2]=1.

opt[3]

specifies instantaneous response modeling if opt[3]=1. The default is opt[3]=0. See the section Multivariate Time Series Analysis for more information.

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 final estimation result, while the print=2 option prints intermediate and final results.

The TSMULMAR subroutine returns the following values:

arcoef

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

ev

refers to the error variance matrix.

nar

is the selected VAR order of the minimum AIC procedure. If opt[2]=0, nar=maxlag.

aic

refers to the minimum AIC value.

The TSMULMAR subroutine estimates the VAR process by using the minimum AIC method. The widely used VAR order selection method is added to the original TIMSAC program, which considers only the possibilities of zero coefficients at the beginning and end of the model. The TSMULMAR subroutine can also estimate the instantaneous response model. See the section Multivariate Time Series Analysis for details.