Testing semiparametric hypotheses in locally stationary processes
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Date
2011-03-23
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Abstract
In this paper we investigate the problem of testing semi parametric hypotheses in locally stationary processes. The proposed method is based on an empirical version of the L2-distance between
the true time varying spectral density and its best approximation under the null hypothesis. As
this approach only requires estimation of integrals of the time varying spectral density and its
square, we do not have to choose a smoothing bandwidth for the local estimation of the spectral density - in contrast to most other procedures discussed in the literature. Asymptotic normality
of the test statistic is derived both under the null hypothesis and the alternative. We also propose
a bootstrap procedure to obtain critical values in the case of small sample sizes. Additionally, we investigate the finite sample properties of the new method and compare it with the currently
available procedures by means of a simulation study. Finally, we illustrate the performance of the
new test in a data example investigating log returns of the S&P 500.
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Keywords
bootstrap, goodness-of- fit tests, integrated periodogram, L2-distance, locally stationary processes, non stationary processes, semi parametric models, spectral density