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TESTS OF THE MARTINGALE DIFFERENCE HYPOTHESIS USING BOOSTING AND RBF NEURAL NETWORK APPROXIMATIONS

Published online by Cambridge University Press:  17 February 2010

George Kapetanios*
Affiliation:
Queen Mary, University of London
Andrew P. Blake
Affiliation:
Bank of England
*
*Address correspondence to George Kapetanios, Department of Economics, Queen Mary, University of London, Mile End Road, London E1 4NS, UK; e-mail: G.Kapetanios@qmul.ac.uk.

Abstract

The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function (RBF) neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a, 2003b). However, unlike that work we provide a formal theoretical justification for the validity of these tests and present some new general theoretical results. These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a, 2003b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have very good power performance. A simplified implementation of boosting is found to have desirable properties and small computational cost. An empirical application to the S&P 500 constituents illustrates the usefulness of our new test.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2010

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