2020/10/26 by Tetsuya Kawai, Kawai, Tetsuya, Masayuki Uchida +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2010.13410
openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.