BDSTEST Procedure

@BDSTest performs the Brock, Dechert, Scheinkman test for i.i.d. The series being tested should be something that reasonably could be thought to be i.i.d. (such as residuals or market returns). Note that there are relatively few theories that would predict i.i.d. (as opposed to weaker criteria like lack of serial correlation) and rejecting i.i.d. will not necessarily help to determine how i.i.d. fails.

@BDSTest( options ) series start end

Parameters

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

Options

P =multiple of standard error (or sample range) to use for the closeness threshold [1.0]

DIM=embedding dimension [depends upon number of data points]

RANGE/[NORANGE]

If RANGE, the threshold is the multiple P of the observed range (max-min) of the series. In that case, P should be less than 1.

[PRINT]/NOPRINT

Variables Defined

%CDSTAT	BDS test statistic (asymptotically N(0,1)) (REAL)
%SIGNIF	Asymptotic p-value (REAL)

Example

This does several several BDS tests with different closeness thresholds and embedding dimensions on the residuals from an AR(1) on log stock returns.

linreg ibmlog

# constant ibmlog{1}

dofor [real] p = 1.5 1.0

do dim=2,5

@bdstest(p=p,dim=dim) %resids

end do dim

end dofor

Output

This is the output from the last combination above (DIM=5 and P=1.0). The test very strongly rejects i.i.d.

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BDS Test for %RESIDS

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P = 1.00000

eps = 0.06615

m = 5

C_mT = 0.07026

C_T = 0.55966

K = 0.35133

sigma2 = 0.00581

BDS = 5.91786

signif = 3.26162e-09

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