Specification Tests for Nonlinear Dynamic Models

Igor Kheifets

No 1937, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C12 C22 C52 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2014-03, Revised 2014-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Specification tests for nonlinear dynamic models (2015)
Working Paper: Specification Tests for Nonlinear Dynamic Models (2014)
Working Paper: Specification Tests for Nonlinear Dynamic Models (2014)
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