Adaptive testing method for ergodic diffusion processes based on high frequency data

Tetsuya Kawai; Masayuki Uchida

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arXiv · 2010.13410

Adaptive testing method for ergodic diffusion processes based on high frequency data

Tetsuya Kawai·Masayuki Uchida

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Abstract

We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the adaptive estimator and provide three types of test statistics: likelihood ratio type test, Wald type test and Rao's score type test. It is proved that these test statistics converge in distribution to the chi-squared distribution under null hypothesis and have consistency of the tests against alternatives. Moreover, these test statistics converge in distribution to the non-central chi-squared distribution under local alternatives. We also give some simulation studies of the behavior of the three types of test statistics.

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Tetsuya Kawai, Masayuki Uchida. 2020-10-26. Adaptive testing method for ergodic diffusion processes based on high frequency data. https://arxiv.org/abs/2010.13410

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