The problem addressed in this paper is to test the null hypothesis
that a time series process is uncorrelated up to lag K
in the presence of statistical dependence. We propose an extension
of the Box–Pierce Q-test that is asymptotically
distributed as chi-square when the null is true for a very general
class of dependent processes that includes non-martingale
difference sequences. The test is based on a consistent estimator
of the asymptotic covariance matrix of the sample autocorrelations
under the null. The finite sample performance of this extension
is investigated in a Monte Carlo study.
This article investigates the finite-sample performance of a modified Box-Pierce Q statistic (Q * ) for testing that financial time series are uncorrelated without assuming statistical independence. The finite-sample rejection probabilities of the Q * test under the null and its power are examined in experiments using time series generated by an MA (1) process where the errors are generated by a GARCH (1, 1) model and by a long memory stochastic volatility model. The tests are applied to daily currency returns.
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