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Specification Tests for Nonlinear Dynamic Models

Author

Listed:
  • Igor Kheifets

    (New Economic School, Moscow)

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.

Suggested Citation

  • Igor Kheifets, 2014. "Specification Tests for Nonlinear Dynamic Models," Working Papers w0209, Center for Economic and Financial Research (CEFIR).
    • Handle: RePEc:cfr:cefirw:w0209
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    File URL: http://www.cefir.ru/papers/WP209.pdf
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    References listed on IDEAS

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    Cited by:

    1. Kheifets, Igor & Velasco, Carlos, 2017. "New goodness-of-fit diagnostics for conditional discrete response models," Journal of Econometrics, Elsevier, vol. 200(1), pages 135-149.
    2. Giovanni Angelini & Luca De Angelis, 2017. "PARX model for football match predictions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(7), pages 795-807, November.
    3. Igor Kheifets, 2011. "Goodness-of-fit testing (in Russian)," Quantile, Quantile, issue 9, pages 25-34, July.
    4. Carlos Velasco, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 237-239, June.
    5. Kheifets, Igor L., 2018. "Multivariate specification tests based on a dynamic Rosenblatt transform," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 1-14.

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    More about this item

    Keywords

    Conditional distribution; Time series; Goodness-of-fit; Empirical process; Weak convergence; Parameter uncertainty; Probability integral transform;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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