Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

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.

Was this topic helpful?