# archtest

Engle test for residual heteroscedasticity

## Syntax

## Description

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

= archtest(`res`

)`res`

.

returns the table `StatTbl`

= archtest(`Tbl`

)`StatTbl`

containing variables for the test results,
statistics, and settings from conducting Engle's ARCH test for residual heteroscedasticity
in the last variable of the input table or timetable `Tbl`

. To select a
different variable in `Tbl`

to test, use the
`DataVariable`

name-value argument.

`[___] = archtest(___,`

specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
`Name=Value`

)`archtest`

returns the output argument combination for the
corresponding input arguments.

Some options control the number of tests to conduct. The following conditions apply when
`archtest`

conducts multiple tests:

For example, ```
archtest(Tbl,DataVariable="ResidualGDP",Alpha=0.025,Lags=[1
4])
```

conducts two tests, at a level of significance of 0.025, for the presence of
heteroscedasticity in the variable `ResidualGDP`

of the table
`Tbl`

. The first test includes `1`

lag in the AR model
of the squared residuals, and the second test includes `4`

lags.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

To draw valid inferences from the test, determine a suitable number of lags by following this procedure:

Fit a sequence of ARCH(

*L*) models by using`arima`

,`garch`

,`egarch`

, or`gjr`

models and its corresponding`estimate`

function. 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.

Evaluate the significance of each restriction by using

`lratiotest`

. Alternatively, compute information criteria using`aicbic`

and combine them with measures of fit.

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

`archtest`

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

.GARCH(

*P*,*Q*) processes are locally equivalent to ARCH(*P*+*Q*) processes. If`archtest(res,Lags=L)`

shows evidence of conditional heteroscedasticity in residuals from a mean model, consider using a GARCH(*P*,*Q*) model with*P*+*Q*=`L`

.

## References

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

[2] Engle, Robert. F. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” *Econometrica* 50 (July 1982): 987–1007. https://doi.org/10.2307/1912773.

## Version History

**Introduced before R2006a**