2018/01/15 by Alessandro De Gregorio, Stefano M. Iacus, De Gregorio, Alessandro +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1801.04848
openalex publication_date 2018/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential equations (i.e. local gaussian approximation of the transition functions) and define a test statistic by means of the empirical L2-distance between quasi-likelihoods. We prove that the introduced test statistic is asymptotically distribution free; namely it weakly converges to a χ2 random variable. Furthermore, we study the power under local alternatives of the parametric test. We show by the Monte Carlo analysis that, in the small sample case, the introduced test seems to perform better than other tests proposed in literature.