MCLEODLI Procedure

@MCLEODLI performs the McLeod-Li test for nonlinearity (ARCH effects). It's a commonly used diagnostic on the standardized residuals from a GARCH model to test for remaining ARCH effects. This test is actually quite simple (it's just a CORRELATE applied to the squares of the series), but we provide this for convenience.

Note that you apply the procedure to the standardized residuals, not to their squares. (The procedure handles the squaring).

@McLeodLi( options) x start end

Parameters

x	series to analyze
start, end	range to analyze. By default, the defined range of x

Options

NUMBER=number of autocorrelations on the squares [10]

DFC=degrees of freedom correction [0]

For residuals from a univariate GARCH model, this should be the number of estimated "GARCH" parameters (those on lagged variance and lagged squared residuals).

TITLE="title for report" ["McLeod-Li Test for Series x"]

[PRINT]/NOPRINT

Variables Defined

%CDSTAT	Test statistic (REAL)
%SIGNIF	Significance level of %CDSTAT (as a chi-squared) (REAL)
%NOBS	Number of observations (INTEGER)

Example

* Tsay, Analysis of Financial Time Series, 3rd edition

* Example 4.3 from pp 182-184

open data d-ibmvwewsp6203.txt

data(format=prn,nolabels,org=columns) 1 10446 date ibm vw ew sp500

set r = 100.0*ibm

garch(reg,p=1,q=1,resids=u,hseries=h) / r

# constant r{2}

* Diagnostics

set ustd = u/sqrt(h)

@regcorrs(nograph,number=20,report) ustd

@mcleodli(number=10,dfc=2) ustd

@mcleodli(number=20,dfc=2) ustd

Sample Output

The 10-2 shows that the statistics were computed with 10 correlations with a degrees of freedom correction of 2. The GARCH instruction in the example uses p=1, q=1, thus the 2. You don't count the variance constant or the mean parameters for the adjustment.

McLeod-Li Test for Series USTD

Using 10444 Observations from 3 to 10446

Test Stat Signif

McLeod-Li(10-2) 13.6054773 0.09265