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.
