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**CALL TSMULMAR(***arcoef, ev, nar, aic, data*

*<,maxlag, opt, missing, print>***);**

The inputs to the TSMULMAR subroutine are as follows:

*data*- specifies a
*T*×*M*data matrix, where*T*is the number of observations and*M*is the number of variables to be analyzed. *maxlag*- specifies the maximum lag of the VAR process.
This value should be less than
[1/2
*M*] 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]=-1. An*M*×1 intercept vector is estimated if*opt*[1]=1. If*opt*[1]=0, the original input data is 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
*M*×(*M** nar) 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 "Multivariate Time Series Analysis" section for details.

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