Data-driven smooth tests for the martingale difference hypothesis

A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distribution-free, with critical values that are already tabulated. The smooth tes...

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Bibliographic Details
Published in:Computational statistics & data analysis 2010-08, Vol.54 (8), p.1983-1998
Main Authors: Escanciano, Juan Carlos, Mayoral, Silvia
Format: Article
Language:English
Subjects:
Asymptotic properties
Computer simulation
Convergence
Data processing
Empirical processes
Exact sciences and technology
General topics
Market efficiency
Martingales
Mathematics
Multivariate analysis
Neyman’s tests
Nonlinear time series
Nonlinear time series Empirical processes Pivotal tests Neyman's tests Semiparametric efficiency Market efficiency
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Optimization
Pivotal tests
Probability and statistics
Probability theory and stochastic processes
Raw materials
Sciences and techniques of general use
Semiparametric efficiency
Statistics
Stochastic processes
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Summary:A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distribution-free, with critical values that are already tabulated. The smooth tests are shown to be optimal in a semiparametric sense discussed in the paper, and they are robust to conditional heteroscedasticity of unknown form. A simulation study shows that the data-driven smooth tests perform very well for a wide range of realistic alternatives and have more power than omnibus and other competing tests. Finally, an application to the S&P 500 stock index and some of its components highlights the merits of our approach. The paper also contains a new weak convergence theorem that is of independent interest.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2010.02.023