# mq: Multivariate Ljung-Box Q Statistics In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

## Description

Computes the multivariate Ljung-Box statistics for cross-correlation matrices

## Usage

 `1` ```mq(x, lag = 24, adj = 0) ```

## Arguments

 `x` The data matrix of a vector time series or residual series of a fitted multivariate model. `lag` The number of cross-correlation matrices used. Default is 24. `adj` Adjustment for the degrees of freedom for the Ljung-Box statistics. This is used for residual series. Default is zero.

## Details

Computes the multivariate Ljung-Box statistics and their p-values. For model checking, the subcommand adj can be used to adjust the degrees of freedom of the Chi-square statistics.

## Value

The multivariate Q-statistics and their p-values. Also, it provides a plot of the p-values.

Ruey S. Tsay

## References

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

## Examples

 ```1 2``` ```x=matrix(rnorm(1500),500,3) mq(x) ```

### Example output

```Ljung-Box Statistics:
m       Q(m)     df    p-value
[1,]   1.00      4.42    9.00     0.88
[2,]   2.00     13.03   18.00     0.79
[3,]   3.00     18.37   27.00     0.89
[4,]   4.00     27.24   36.00     0.85
[5,]   5.00     33.95   45.00     0.89
[6,]   6.00     46.48   54.00     0.76
[7,]   7.00     49.40   63.00     0.89
[8,]   8.00     65.25   72.00     0.70
[9,]   9.00     73.29   81.00     0.72
[10,]  10.00     85.00   90.00     0.63
[11,]  11.00     95.33   99.00     0.59
[12,]  12.00    102.68  108.00     0.63
[13,]  13.00    113.61  117.00     0.57
[14,]  14.00    119.66  126.00     0.64
[15,]  15.00    133.50  135.00     0.52
[16,]  16.00    141.98  144.00     0.53
[17,]  17.00    148.44  153.00     0.59
[18,]  18.00    159.71  162.00     0.54
[19,]  19.00    170.10  171.00     0.51
[20,]  20.00    176.15  180.00     0.57
[21,]  21.00    180.80  189.00     0.65
[22,]  22.00    184.78  198.00     0.74
[23,]  23.00    195.56  207.00     0.71
[24,]  24.00    204.93  216.00     0.69
```

MTS documentation built on Oct. 10, 2018, 5:04 p.m.