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Asymptotically optimal tests for non-linear autoregressive model with β-ARCH errors

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  • Laïb, Naâmane
  • Lounis, Tewfik

Abstract

This paper develops optimal statistical tests for testing certain class of non-linear time series models contiguous to a non-linear autoregressive processes with β-ARCH errors. The statistical tests are based on the Local Asymptotic Normality -LAN-(established via the quadratic mean differentiability) of the log-likelihood ratio of the studied Model when its parameters are estimated. Their local power are also computed. Some examples related to financial models are considered. Our approach uses mainly an efficient estimators of Bouzebda and Lounis (2019).

Suggested Citation

  • Laïb, Naâmane & Lounis, Tewfik, 2021. "Asymptotically optimal tests for non-linear autoregressive model with β-ARCH errors," Statistics & Probability Letters, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:stapro:v:178:y:2021:i:c:s0167715221001462
    DOI: 10.1016/j.spl.2021.109184
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    References listed on IDEAS

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    1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    2. Hwang, Sun Y. & Basawa, I. V., 2001. "Nonlinear time series contiguous to AR(1) processes and a related efficient test for linearity," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 381-390, May.
    3. An, Hongzhi & Chen, Min & Huang, Fuchun, 1997. "The geometric ergodicity and existence of moments for a class of non-linear time series model," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 213-224, January.
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