A model specification test for nonlinear stochastic diffusions with delay

Zongwu Cai (), Hongwei Mei () and Rui Wang ()
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Zongwu Cai: The University of Kansas
Hongwei Mei: Texas Tech University
Rui Wang: The University of Kansas

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 3, No 8, 795-812

Abstract: Abstract This paper investigates model specification problems for nonlinear stochastic differential equations with delay (SDDE). Compared to the model specification for conventional stochastic diffusions without delay, the observed sequence does not admit a Markovian structure so that the classical testing procedures may not be applicable. To overcome this difficulty, a moment estimator is newly proposed based on the ergodicity of SDDEs and its asymptotic properties are established. Based on the proposed moment estimator, a testing procedure is proposed for our model specification testing problems. Particularly, the limiting distributions of the proposed test statistic are derived under null hypotheses and the test power is examined under some specific alternative hypotheses. Finally, a Monte Carlo simulation is conducted to illustrate the finite sample performance of the proposed test.

Keywords: Model specification test; Stochastic differential equation with delay; Moment estimator; Ergodicity; Invariant measure; Non-Markovian property; Primary 62F05; Secondary 62M07 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-024-09309-2

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