ARCHTEST—Test for ARCH/GARCH effects

[TomDoan]

@ARCHTEST does the Engle test for ARCH effects by regressing the square of a series on its lags and testing the significance of the lags. The null is that the series is mean zero, not serially correlated and has constant variance. This can be used to test the original series for ARCH (or GARCH) by applying it to residuals from a preliminary LINREG (to satisfy the requirement that the series be mean zero and not serially correlated). It can also be used as a diagnostic by applying it to the standardized residuals from GARCH estimation. Note that you apply the procedure to the residuals, not to their squares. (The procedure handles the squaring).

A multivariate version is available with @MVARCHTEST.

Detailed description

[upani]

Hi All,

I want to do ARCH test to a univariate time series to decide whether Garch (1,1) model can be applied to the data set or not. I have used the following command:

Code: Select all

open data 'ndata2.xlsx'
calendar(a) 1987
data(format=xlsx,org=columns) 1987 2013 Price

set ret = 100*log(Price/Price{1})
linreg(noprint) ret / resids
# constant
set res = resids

source archtest.src
@archtest(lags=12,span=1) res

I got the following output.

Code: Select all

Test for ARCH in RES
Using data from 1988:01 to 2013:01

Lags Statistic Signif. Level
   1     2.063       0.16439
   2     0.975       0.39372
   3     0.545       0.65725
   4     0.356       0.83619
   5     7.292       0.00120
   6     7.387       0.00133
   7     5.909       0.00486
   8     4.599       0.01754
   9     4.019       0.04008
  10     2.821       0.13193
  11     1.722       0.36025
  12     0.845       0.70191

I want to know the interpretation for the above result. I am confused as for some lag it is significant and some lag it is not significant. Would you please clarify the doubt. I have gone through the GARCH course material which i have purchased from Estima. I did not get any answer to my problem.

With sincere regards,
Upananda

[TomDoan]

Is this actually annual data? Annual data rarely has GARCH properties. Given that there is nothing in the short lags, there is no reason to believe that a GARCH model will work. That looks a lot like very noisy data with at least a few large outliers separated by five observations.

[Max Resende]

Dear RATS users,

I want to do an @ARCHTEST to a univariate time series as a preliminary test to decide whether a Garch model can be applied to the data set or not. I have used the following command:

Code: Select all

* ARCH Test
linreg r / resids
# constant
@archtest(lags=6,form=lm,span=1) resids

I got these results:

Code: Select all

Test for ARCH in RESIDS
Using data from 2010:01:05 to 2018:12:28

Lags Statistic Signif. Level
   1    65.096       0.00000
   2   114.418       0.00000
   3   134.175       0.00000
   4   139.460       0.00000
   5   147.649       0.00000
   6   150.318       0.00000

I would like to know if my interpretation is correct:
Since the Lagrange multiplier test coefficients are significant, that means that I might have a GARCH Process (residuals are not constant).

Best regards,

Max

[TomDoan]

Yes. (Residuals are not constant variance),