Evidential inference for diffusion-type processes

Abstract

This article analyses diffusion-type processes from a new point-of-view. Consider two statistical hypotheses on a diffusion process. We do not use a classical test to reject or accept one hypothesis using the Neyman–Pearson procedure and do not involve Bayesian approach. As an alternative, we propose using a likelihood paradigm to characterizing the statistical evidence in support of these hypotheses. The method is based on evidential inference introduced and described by Royall [Royall R. Statistical evidence: a likelihood paradigm. London: Chapman and Hall; 1997]. In this paper, we extend the theory of Royall to the case when data are observations from a diffusion-type process instead of iid observations. The empirical distribution of likelihood ratio is used to formulate the probability of strong, misleading and weak evidences. Since the strength of evidence can be affected by the sampling characteristics, we present a simulation study that demonstrates these effects. Also we try to control misleading evidence and reduce them by adjusting these characteristics. As an illustration, we apply the method to the Microsoft stock prices.

Keywords:

• diffusion-type processes
• evidential paradigm
• the law of likelihood
• likelihood ratios
• statistical evidence
• misleading evidence

AMS Subject Classifications:

• 62A99
• 62F03
• 62M02

Acknowledgments

The authors would like to thank the unknown referee for the critical comments and suggestions which helped to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).