# serial.test {vars}

### 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.

L__tkepohl, 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.

### See Also

`VAR`

, `vec2var`

, `plot`

### Examples

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

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