Specification Tests for Nonlinear Dynamic Models

28 Pages Posted: 31 Mar 2015

Multiple version iconThere are 2 versions of this paper

Date Written: February 2015


We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any set‐up where parametric conditional distribution of the data is specified and, 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 behaviour in conditional distribution and does not rely on smoothing techniques that 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, Empirical process, Goodness‐of‐fit, Parameter uncertainty, Probability integral transform, Time series, Weak convergence

Suggested Citation

Kheifets, Igor, Specification Tests for Nonlinear Dynamic Models (February 2015). The Econometrics Journal, Vol. 18, Issue 1, pp. 67-94, 2015. Available at SSRN: https://ssrn.com/abstract=2587463 or http://dx.doi.org/10.1111/ectj.12040

Igor Kheifets (Contact Author)

New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026

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