SCTEST.RPF

SCTEST.RPF provides examples of several different tests for (univariate) serial correlation. This uses one of the series from West and Cho(1995).

The raw data are (log) weekly exchange rates, which are transformed to weekly returns. The specific series used is the Canadian $ to US $.

set xcan = 100.0*(scan-scan{1})

First up is is a battery of Q tests using CORRELATE with the QSTATS option. (Output).

correlate(qstats,number=40,span=10) xcan

Next, it does the same type of test using the procedure @REGCORRS, which also will produce both a table of correlations and tests, and a graph of the autocorrelations. The overall impression here is that there may be some autocorrelation at lag 1 (only) that might be worth some attention.

@regcorrs(number=40,graph,report,nocrit,$

title="Correlations of Can$ Exchange Rate") xcan

The West-Cho test does a form of Q test allowing for heteroscedasticity in the series. (Output). This fails to reject at any standard significance level.

@westchotest(number=40) xcan

The cumulated periodogram test does a test for white noise in the frequency domain. This provides both a report on the Kolmogorov-Smirnov test, and a graph of the difference between the observed spectrum and the spectrum of white noise. The largest gap is between the .01 and .05 significance level.

@cumpdgm xcan

Full Program

open data westcho_xrate.xls
calendar(w) 1973:3:7
data(format=xls,org=col) 1973:03:07 1989:09:20 scan sfra sger sita sjap sukg
*
set xcan = 100.0*(scan-scan{1})
*
* Battery of Q tests done using CORRELATE
*
correlate(qstats,number=40,span=10) xcan
*
* Same thing using @REGCORRS
*
@regcorrs(number=40,graph,report,nocrit,$
title="Correlations of Can$ Exchange Rate") xcan
*
* Using @WestChoTest
*
@westchotest(number=40) xcan
*
* Using @CUMPDGM
*
@cumpdgm xcan

Output

Correlations of Series XCAN

Weekly Data From 1973:03:14 To 1989:09:20

Autocorrelations

1 2 3 4 5 6 7 8 9 10

0.09126 0.01059 -0.00433 -0.04290 -0.01938 -0.03114 -0.03731 0.00089 -0.01085 -0.02078

11 12 13 14 15 16 17 18 19 20

0.05172 0.03756 0.02916 0.01617 -0.01652 0.05850 -0.00925 0.01757 0.00209 0.00268

21 22 23 24 25 26 27 28 29 30

-0.00872 0.00209 -0.01499 0.06401 0.01788 -0.01342 0.01629 -0.01860 -0.02384 -0.01520

31 32 33 34 35 36 37 38 39 40

-0.07605 0.01279 0.04600 0.04894 0.08262 0.05039 -0.01168 -0.06981 0.00250 0.04865

Ljung-Box Q-Statistics

Lags Statistic Signif Lvl

10 11.793 0.299157

20 19.966 0.460074

30 25.590 0.695899

40 50.117 0.131165

Lag Corr Partial LB Q Q Signif

1 0.091 0.091 7.209804 0.0073

2 0.011 0.002 7.308005 0.0259

3 -0.004 -0.006 7.323984 0.0623

4 -0.043 -0.042 8.919572 0.0631

5 -0.019 -0.012 9.246691 0.0996

6 -0.031 -0.028 10.087041 0.1210

7 -0.037 -0.032 11.299815 0.1261

8 0.001 0.006 11.300310 0.1853

9 -0.011 -0.013 11.405961 0.2489

10 -0.021 -0.022 11.783392 0.2998

11 0.051 0.052 14.100607 0.2275

12 0.037 0.027 15.309519 0.2249

13 0.029 0.020 16.052296 0.2463

14 0.016 0.009 16.280284 0.2966

15 -0.017 -0.016 16.524787 0.3481

16 0.058 0.064 19.482190 0.2445

17 -0.009 -0.016 19.554643 0.2976

18 0.018 0.027 19.834022 0.3422

19 0.002 0.000 19.838705 0.4043

20 0.002 0.009 19.843630 0.4677

21 -0.008 -0.006 19.905371 0.5273

22 0.003 0.007 19.911332 0.5886

23 -0.015 -0.013 20.102517 0.6357

24 0.063 0.064 23.683289 0.4798

25 0.017 0.005 23.954328 0.5220

26 -0.013 -0.012 24.099175 0.5703

27 0.016 0.012 24.325604 0.6122

28 -0.019 -0.018 24.646797 0.6470

29 -0.024 -0.023 25.158258 0.6700

30 -0.014 -0.011 25.340680 0.7083

31 -0.075 -0.069 30.434890 0.4949

32 0.012 0.019 30.563783 0.5392

33 0.045 0.043 32.371697 0.4982

34 0.049 0.042 34.559412 0.4410

35 0.082 0.063 40.596516 0.2373

36 0.049 0.028 42.727440 0.2045

37 -0.011 -0.019 42.836746 0.2350

38 -0.068 -0.073 47.039849 0.1492

39 0.002 0.029 47.041893 0.1765

40 0.047 0.050 49.044173 0.1546

West-Cho Modified Q Test, Series XCAN

Q(40) 44.16

Signif. 0.3001

Cumulated Periodogram Test for Series XCAN

Maximum Gap 0.0692

At Frequency 1.1474

Approximate Rejection Limits

1% 0.0720

5% 0.0601

10% 0.0539

Graphs