Specification Tests for Nonlinear Dynamic Models

37 Pages Posted: 4 Mar 2014 Last revised: 15 Oct 2014

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Date Written: October 13, 2014

Abstract

We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behavior in conditional distribution and does not rely on smoothing techniques which require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite-sample size and power properties. Using the new test and graphical tools we check the adequacy of various popular heteroscedastic models for stock exchange index data.

Keywords: Conditional distribution, Time series, Goodness-of-fit, Empirical process, Weak convergence, Parameter uncertainty, Probability integral transform

JEL Classification: C12, C22, C52

Suggested Citation

Kheifets, Igor, Specification Tests for Nonlinear Dynamic Models (October 13, 2014). Cowles Foundation Discussion Paper No. 1937. Available at SSRN: https://ssrn.com/abstract=2404003 or http://dx.doi.org/10.2139/ssrn.2404003

Igor Kheifets (Contact Author)

New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026
Russia

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