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Maximum likelihood estimation for α-stable double autoregressive models

Author

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  • Li, Dong
  • Tao, Yuxin
  • Yang, Yaxing
  • Zhang, Rongmao

Abstract

The paper investigates the maximum likelihood estimation (MLE) for a first-order double autoregressive model with standardized non-Gaussian symmetric α-stable innovation (sDAR) within a unified framework of stationary and explosive cases. It is shown that the MLE of all parameters, including the stable exponent in the innovation, are strongly consistent and asymptotically normal (with the exception of the intercept for the explosive case). Particularly, the MLE of the parameter in the conditional location is always asymptotically normal, regardless of the stationary or explosive case. This point totally differs from that for linear α-stable AR models in Andrews et al. (2009). Furthermore, it is the first time to provide exact values of the quantities related to the innovation in the asymptotic covariance matrices when the true innovation is the standard Cauchy distribution. Additionally, a modified Kolmogorov-type test statistic is proposed for model diagnostic checking in the stationary case. Monte Carlo simulation studies are conducted to confirm our theoretical findings and assess the finite-sample performance of the MLE and the modified Kolmogorov-type test. An empirical example is analyzed to illustrate the usefulness of sDAR models.

Suggested Citation

  • Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:1:s0304407623001653
    DOI: 10.1016/j.jeconom.2023.04.011
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    References listed on IDEAS

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    More about this item

    Keywords

    DAR model; Kolmogorov-type test; MLE; Nonstationarity; Stable distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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