A Generalized Fast Algorithm for BDS-Type Statistics

Abstract We provide a fast algorithm to calculate the m-dimensional distance histogram on which Brock, Dechert, and Sheinkman's (1987) BDS-type statistics are based. The algorithm generalizes a fast algorithm due to LeBaron by calculating the histogram for any finite set of distances simultaneo...

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Published inStudies in Nonlinear Dynamics & Econometrics Vol. 4; no. 1; p. 2
Main Author Mayer-Foulkes, David
Format Journal Article
LanguageEnglish
Published bepress 01.04.2000
De Gruyter
Subjects
BDS
chaos
fast algorithm
nonlinearity
specification testing
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ISSN1558-3708
1558-3708
DOI10.2202/1558-3708.1055

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Summary:Abstract We provide a fast algorithm to calculate the m-dimensional distance histogram on which Brock, Dechert, and Sheinkman's (1987) BDS-type statistics are based. The algorithm generalizes a fast algorithm due to LeBaron by calculating the histogram for any finite set of distances simultaneously, and also using induction in m. By reordering the calculation appropriately, the algorithm also requires less memory and time. The two algorithms are compared using LeBaron's MS-DOS implementation in C and our Delphi (Windows Pascal) program. The generalized algorithm is faster when more than a few values of m and M (the distance parameter) are required, and is set up to calculate up to 255 values using short-integer arithmetic. Recommended Citation David Mayer-Foulkes (2000) "A Generalized Fast Algorithm for BDS-Type Statistics ", Studies in Nonlinear Dynamics & Econometrics: Vol. 4: No. 1, Algorithm 2. http://www.bepress.com/snde/vol4/iss1/algorithm2 Related Files HomePage.htm (26 kB) Code
Bibliography:istex:9B7C6F9918D54E1F27FE8367DC639341645DF507
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snde.2000.4.1.1055.pdf
ArticleID:1558-3708.1055
ISSN:1558-3708
1558-3708
DOI:10.2202/1558-3708.1055