Bernoulli

Goodness-of-fit tests for Markovian time series models: Central limit theory and bootstrap approximations

Michael H. Neumann and Efstathios Paparoditis

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Abstract

New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that of the model class postulated under the null hypothesis. The model specification under the null allows for Markovian models, the transition mechanisms of which depend on an unknown vector of parameters and an unspecified distribution of i.i.d. innovations. Asymptotic properties of the test statistic are derived and the critical values of the test are found using appropriate bootstrap schemes. General properties of the bootstrap for Markovian processes are derived. A new central limit theorem for triangular arrays of weakly dependent random variables is obtained. For the proof of stochastic equicontinuity of multidimensional empirical processes, we use a simple approach based on an anisotropic tiling of the space. The finite-sample behavior of the proposed test is illustrated by some numerical examples and a real-data application is given.

Article information

Source
Bernoulli, Volume 14, Number 1 (2008), 14-46.

Dates
First available in Project Euclid: 8 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1202492783

Digital Object Identifier
doi:10.3150/07-BEJ6055

Mathematical Reviews number (MathSciNet)
MR2401652

Zentralblatt MATH identifier
1155.62058

Keywords
ARCH processes autoregressive processes bootstrap central limit theorem goodness-of-fit test weak dependence

Citation

Neumann, Michael H.; Paparoditis, Efstathios. Goodness-of-fit tests for Markovian time series models: Central limit theory and bootstrap approximations. Bernoulli 14 (2008), no. 1, 14--46. doi:10.3150/07-BEJ6055. https://projecteuclid.org/euclid.bj/1202492783


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