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A Specification Test Based on Convolution-Type Distribution Function Estimates for Non-Linear Autoregressive Processes

In: Essays in Honor of Joon Y. Park: Econometric Theory

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  • Kun Ho Kim
  • Hira L. Koul
  • Jiwoong Kim

Abstract

This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated square difference between the empirical distribution function estimate and a convolution-type distribution function estimate of the stationary distribution function obtained from the autoregressive residuals. Some asymptotic properties of the proposed convolution-type distribution function estimate are studied when the model’s innovation density is unknown. These properties are in turn used to derive the asymptotic null distribution of the proposed test statistic. We also discuss some finite sample properties of the test statistic based on the block bootstrap methodology. A simulation study shows that the proposed test competes favorably with some existing tests in terms of the empirical level and power.

Suggested Citation

  • Kun Ho Kim & Hira L. Koul & Jiwoong Kim, 2023. "A Specification Test Based on Convolution-Type Distribution Function Estimates for Non-Linear Autoregressive Processes," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 187-206, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-90532023000045a006
    DOI: 10.1108/S0731-90532023000045A006
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    More about this item

    Keywords

    Nonlinear autoregressive processes; integrated squared difference of the two d.f.’s; empirical and convolution d.f. estimators; block bootstrap; asymptotic power; empirical level and power; C12; C13; C14;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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