# VAR: Vector Autoregressive Model In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

## Description

Perform least squares estimation of a VAR model

## Usage

 `1` ```VAR(x, p = 1, output = T, include.mean = T, fixed = NULL) ```

## Arguments

 `x` A T-by-k matrix of k-dimensional time series `p` Order of VAR model. Default is 1. `output` A logical switch to control output. Default is with output. `include.mean` A logical switch. It is true if mean vector is estimated. `fixed` A logical matrix used in constrained estimation. It is used mainly in model simplifcation, e.g., removing insignificant estimates.

## Details

To remove insignificant estimates, one specifies a threshold for individual t-ratio. The fixed matrix is then defined automatically to identify those parameters for removal.

## Value

 `data ` Observed data `cnst ` A logical switch to include the mean constant vector `order ` VAR order `coef ` Coefficient matrix `aic,bic,hq` Information criteria of the fitted model `residuals` Residuals `secoef` Standard errors of the coefficients to be used in model refinement `Sigma ` Residual covariance matrix `Phi ` AR coefficient polynomial `Ph0 ` The constant vector

Ruey S. Tsay

## References

Tsay (2014, Chapter 3). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

refVAR command

## Examples

 ```1 2 3 4``` ```data("mts-examples",package="MTS") gdp=log(qgdp[,3:5]) zt=diffM(gdp) m1=VAR(zt,p=2) ```

### Example output

```Constant term:
Estimates:  0.001258163 0.001231581 0.002895581
Std.Error:  0.0007266338 0.0007382941 0.000816888
AR coefficient matrix
AR( 1 )-matrix
[,1]  [,2]   [,3]
[1,] 0.393 0.103 0.0521
[2,] 0.351 0.338 0.4691
[3,] 0.491 0.240 0.2356
standard error
[,1]   [,2]   [,3]
[1,] 0.0934 0.0984 0.0911
[2,] 0.0949 0.1000 0.0926
[3,] 0.1050 0.1106 0.1024
AR( 2 )-matrix
[,1]   [,2]     [,3]
[1,]  0.0566  0.106  0.01889
[2,] -0.1914 -0.175 -0.00868
[3,] -0.3120 -0.131  0.08531
standard error
[,1]   [,2]   [,3]
[1,] 0.0924 0.0876 0.0938
[2,] 0.0939 0.0890 0.0953
[3,] 0.1038 0.0984 0.1055

Residuals cov-mtx:
[,1]         [,2]         [,3]
[1,] 2.824442e-05 2.654091e-06 7.435286e-06
[2,] 2.654091e-06 2.915817e-05 1.394879e-05
[3,] 7.435286e-06 1.394879e-05 3.569657e-05

det(SSE) =  2.258974e-14
AIC =  -31.13328
BIC =  -30.726
HQ  =  -30.96783
```

MTS documentation built on May 29, 2017, 5:15 p.m.