A Model Specification Test for Nonlinear Stochastic Diffusions with Delay

Zongwu Cai, Hongwei Mei and Rui Wang
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Zongwu Cai: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA
Hongwei Mei: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
Rui Wang: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA

No 202301, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: The 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 fail. To overcome this difficulty, we propose a moment estimator from the ergodicity of SDDEs and its asymptotic properties are established. Based on the proposed moment estimator, a testing procedure is derived 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 obtained 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. (search for similar items in EconPapers)
JEL-codes: C12 C32 C58 (search for similar items in EconPapers)
Date: 2023-01, Revised 2023-01
New Economics Papers: this item is included in nep-ecm
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