Evidential inference for diffusion-type processes. (English) Zbl 1510.62338
Summary: 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 R. M. Royall [Statistical evidence. A likelihood paradigm. London: Chapman & Hall (1997; Zbl 0919.62004)]. 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.
MSC:
| 62M05 | Markov processes: estimation; hidden Markov models |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 62A01 | Foundations and philosophical topics in statistics |
Keywords:
diffusion-type processes; evidential paradigm; law of likelihood; likelihood ratios; statistical evidence; misleading evidenceCitations:
Zbl 0919.62004References:
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