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Asymptotic inference of the ARMA model with time‐functional variance noises

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  • Bibi Cai
  • Enwen Zhu
  • Shiqing Ling

Abstract

This paper studies the autoregressive and moving average (ARMA) model with time‐functional variance (TFV) noises, called the ARMA‐TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA‐TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.

Suggested Citation

  • Bibi Cai & Enwen Zhu & Shiqing Ling, 2024. "Asymptotic inference of the ARMA model with time‐functional variance noises," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1230-1258, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1230-1258
    DOI: 10.1111/sjos.12708
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