# serial.test {vars}

Test for serially correlated errors
Package:
vars
Version:
1.5-2

### Description

This function computes the multivariate Portmanteau- and Breusch-Godfrey test for serially correlated errors.

### Usage

```serial.test(x, lags.pt = 16, lags.bg = 5, type = c("PT.asymptotic",
"PT.adjusted", "BG", "ES") )
```

### Arguments

x
Object of class ‘`varest`’; generated by `VAR()`, or an object of class ‘`vec2var`’; generated by `vec2var()`.
lags.pt
An integer specifying the lags to be used for the Portmanteau statistic.
lags.bg
An integer specifying the lags to be used for the Breusch-Godfrey statistic.
type
Character, the type of test. The default is an asymptotic Portmanteau test.

### Details

The Portmanteau statistic for testing the absence of up to the order h serially correlated disturbances in a stable VAR(p) is defined as: where . The test statistic is approximately distributed as χ^2(K^2(h - p)). This test statistic is choosen by setting `type = "PT.asymptotic"`. For smaller sample sizes and/or values of h that are not sufficiently large, a corrected test statistic is computed as: This test statistic can be accessed, if `type = "PT.adjusted"` is set.

The Breusch-Godfrey LM-statistic is based upon the following auxiliary regressions: The null hypothesis is: H_0: B_1 = ... = B_h = 0 and correspondingly the alternative hypothesis is of the form for i = 1, 2, ..., h. The test statistic is defined as:

where     ilde{Σ}_R and     ilde{Σ}_e assign the residual covariance matrix of the restricted and unrestricted model, respectively. The test statistic LM_h is distributed as χ^2(hK^2). This test statistic is calculated if `type =     "BG"` is used.
Edgerton and Shukur (1999) proposed a small sample correction, which is defined as: with R_r^2 = 1 - |    ilde{Σ}_e | / |    ilde{Σ}_R|, r = ((K^2m^2 - 4)/(K^2 + m^2 - 5))^{1/2}, q = 1/2 K m - 1 and N = T - K - m - 1/2(K - m + 1), whereby n is the number of regressors in the original system and m = Kh. The modified test statistic is distributed as . This modified statistic will be returned, if `type =     "ES"` is provided in the call to `serial()`.

### Values

A list with class attribute ‘`varcheck`’ holding the following elements:

resid
A matrix with the residuals of the VAR.
pt.mul
A list with objects of class attribute ‘`htest`’ containing the multivariate Portmanteau-statistic (asymptotic and adjusted.
LMh
An object with class attribute ‘`htest`’ containing the Breusch-Godfrey LM-statistic.
LMFh
An object with class attribute ‘`htest`’ containing the Edgerton-Shukur F-statistic.

### References

Breusch, T . S. (1978), Testing for autocorrelation in dynamic linear models, Australian Economic Papers, 17: 334-355. Edgerton, D. and Shukur, G. (1999), Testing autocorrelation in a system perspective, Econometric Reviews, 18: 43-386.

Godfrey, L. G. (1978), Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables, Econometrica, 46: 1303-1313. Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.

Ltkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

### Note

This function was named `serial` in earlier versions of package vars; it is now deprecated. See `vars-deprecated` too.

`VAR`, `vec2var`, `plot`

### Examples

```data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
serial.test(var.2c, lags.pt = 16, type = "PT.adjusted")```

### Author(s)

Bernhard Pfaff

Documentation reproduced from package vars, version 1.5-2. License: GPL (>= 2)