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Engle test for residual heteroscedasticity

`h = archtest(res)`

`h = archtest(res,Name,Value)`

```
[h,pValue]
= archtest(___)
```

```
[h,pValue,stat,cValue]
= archtest(___)
```

returns
a logical value with the rejection decision from conducting the Engle’s
ARCH test for residual heteroscedasticity in the univariate
residual series `h`

= archtest(`res`

)`res`

.

uses
additional options specified by one or more `h`

= archtest(`res`

,`Name,Value`

)`Name,Value`

pair
arguments.

If any

`Name,Value`

pair argument is a vector, then all`Name,Value`

pair arguments that you specify must be vectors of equal length or scalars.`archtest(res,Name,Value)`

treats each element of a vector input as a separate test, and returns a vector of rejection decisions.If any

`Name,Value`

pair argument is a row vector, then`archtest(res,Name,Value)`

returns row vectors.

You must determine a suitable number of lags to draw valid inferences from Engle’s ARCH test. One method is to:

Fit a sequence of

`arima`

,`garch`

,`egarch`

, or`gjr`

models using`estimate`

. Restrict each model by specifying progressively smaller ARCH lags (i.e., ARCH effects corresponding to increasingly smaller lag polynomial terms).Obtain loglikelihoods from the estimated models.

Use

`lratiotest`

to evaluate the significance of each restriction. Alternatively, determine information criteria using`aicbic`

and combine them with measures of fit.

Residuals in an ARCH process are dependent, but not correlated. Thus,

`archtest`

tests for heteroscedasticity without autocorrelation. To test for autocorrelation, use`lbqtest`

.GARCH(

*P*,*Q*) processes are locally equivalent to ARCH(*P*+*Q*) processes. If`archtest(res,'lags',lags)`

shows evidence of conditional heteroscedasticity in residuals from a mean model, then it might be better to model a GARCH(*P*,*Q*) model with*P*+*Q*=`lags`

.

[1] Box, G. E. P., G.M. Jenkins, and G.C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[2] Engle, R. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation." Econometrica. Vol. 96, 1988, pp. 893–920.

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