Abstract
In this paper, we consider inference problem about the drift parameter vector in generalized mean reverting processes with multiple and unknown change-points. In particular, we study the case where the parameter may satisfy uncertain restriction. As compared to the results in literature, we generalize some findings in five ways. First, we consider the model which incorporates the uncertain prior knowledge. Second, we derive the unrestricted estimator (UE) and the restricted estimator (RE) and we study their asymptotic properties. Third, we derive a test for testing the hypothesized restriction and we derive its asymptotic local power. We also prove that the proposed test is consistent. Fourth, we construct a class of shrinkage type estimators (SEs) which encloses the UE, the RE and classical SEs. Fifth, we derive the relative risk dominance of the proposed estimators. More precisely, we prove that the SEs dominate the UE. Finally, we present some simulation results which corroborate the established theoretical findings.
Highlights
Nowadays, the Ornstein-Uhlenbeck (O-U) process is applied in different fields, such as physical sciences (Lansky and Sacerdote (2001)) [11] and biology (Rohlfs et al (2010)) [17]
The novelty of the proposed test and its asymptotic power consists in the fact that, their derivation is not based on the joint asymptotic normality between θ(φ, m ) and θ(φ, m ), as this is the case in Saleh (2006) [18], Nkurunziza (2012) [14], Nkurunziza and Zhang (2018) [15] and references therein
We proposed improved estimation and testing methods in generalized O-U processes with multiple unknown change-points when the drift parameter satisfies uncertain constraint
Summary
The Ornstein-Uhlenbeck (O-U) process is applied in different fields, such as physical sciences (Lansky and Sacerdote (2001)) [11] and biology (Rohlfs et al (2010)) [17]. To solve such a problem, Dehling et al (2010) [6] proposed generalized Ornstein-Uhlenbeck processes which have a time-dependent periodic mean reverting function. Chen et al (2017) [4] proposed a method for detecting multiple change points in generalized O-U processes. We study the inference problem in generalized O-U processes with multiple unknown change points in the context where the drift parameter is suspected to satisfy some restrictions. For the convenience of the reader, some technical results and proofs are given in the Appendix A
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