# VMAorder: VMA Order Specification In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

## Description

Performs multivariate Ljung-Box tests to specify the order of a VMA process

## Usage

 `1` ```VMAorder(x, lag = 20) ```

## Arguments

 `x` Data matrix of the observed k-dimensional time series. Each column represents a time series. `lag` The maximum VMA order entertained. Default is 20.

## Details

For a given lag, the command computes the Ljung-Box statistic for testing rho_j = ... = rho_lag = 0, where j = 1, 2, ..., lag. For a VMA(q) process, the Ljung-Box statistics should be significant for the first q lags, and insignificant thereafter.

## Value

The Q-statistics and p-value plot

Ruey S. Tsay

## References

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

## Examples

 ```1 2``` ```zt=matrix(rnorm(600),200,3) VMAorder(zt) ```

### Example output

```Q(j,m) Statistics:
j     Q(j,m)   p-value
[1,]   1.00    197.13     0.18
[2,]   2.00    191.57     0.13
[3,]   3.00    185.95     0.10
[4,]   4.00    181.99     0.05
[5,]   5.00    171.40     0.06
[6,]   6.00    157.63     0.09
[7,]   7.00    145.80     0.11
[8,]   8.00    133.41     0.14
[9,]   9.00    124.90     0.13
[10,]  10.00    118.27     0.09
[11,]  11.00    102.37     0.18
[12,]  12.00     98.64     0.09
[13,]  13.00     88.90     0.09
[14,]  14.00     73.46     0.17
[15,]  15.00     69.96     0.07
[16,]  16.00     59.70     0.07
[17,]  17.00     43.91     0.17
[18,]  18.00     37.06     0.09
[19,]  19.00     24.65     0.13
[20,]  20.00      8.53     0.48
```

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