ADTEST Procedure

@ADTEST performs the Anderson-Darling test for normality. This compares the empirical distribution function (EDF) with the theoretical Normal distribution function.

@ADTest( options ) x start end

Parameters

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

Options

MEAN=mean of assumed distribution [sample mean]

VARIANCE=variance of assumed distribution [sample variance]

Variables Defined

%CDSTAT	test statistic (REAL)
%SIGNIF	approximate significance level (REAL)

Reference

Stephens, M. A. (1974). "EDF Statistics for Goodness of Fit and Some Comparisons", Journal of the American Statistical Association, Vol. 69, pp. 730-737.

Example

This is based upon the GARCHUV.RPF sample program.

open data garch.asc

data(format=free,org=columns) 1 1867 bp cd dm jy sf

set dlogdm = 100*log(dm/dm{1})

* Estimate a GARCH(1,1) with an AR(1) mean model, saving the residuals

* and variance estimates.

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

# constant dlogdm{1}

* Do diagnostics on the standardized residuals.

set ustd = u/sqrt(h)

set ustdsq = ustd^2

@regcorrs(qstat,number=40,dfc=1,title="GARCH-LB Test") ustd

@regcorrs(qstat,number=40,dfc=2,title="GARCH-McLeod-Li Test") ustdsq

stats ustd

@adtest ustd

Sample Output

The first table is the output from the STATISTICS instruction in the example, the second is for the AD test. The Jarque-Bera test here rejects normality (because of the high kurtosis), while the A-D test accepts it.

Statistics on Series USTD

Quarterly Data From 1947:03 To 1989:01

Observations 167

Sample Mean -0.027803 Variance 0.973454

Standard Error 0.986637 SE of Sample Mean 0.076348

t-Statistic (Mean=0) -0.364162 Signif Level (Mean=0) 0.716200

Skewness -0.038943 Signif Level (Sk=0) 0.838663

Kurtosis (excess) 1.913007 Signif Level (Ku=0) 0.000001

Jarque-Bera 25.506911 Signif Level (JB=0) 0.000003

Anderson-Darling Test for Normality

Series USTD

Observations 167

AD Statistic 1.6259

Signif Level 0.1445