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An alternative sequential method for the state estimation of a partially observed SETAR(1) process

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  • Milheiro-Oliveira, Paula

Abstract

We discuss a novel sequential test based on the quadratic variation of the observations to decide which regime governs the dynamics of the non-observed process in a filtering problem with small observation noise. The non-observed state process is a self-exciting threshold autoregressive process of order one (SETAR(1)) with two regimes. The observation function is not one-to-one. The proposed procedure performs well and may be competitive in some applications.

Suggested Citation

  • Milheiro-Oliveira, Paula, 2022. "An alternative sequential method for the state estimation of a partially observed SETAR(1) process," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000128
    DOI: 10.1016/j.spl.2022.109385
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    References listed on IDEAS

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    1. Alexandre Brouste & Chunhao Cai & Marius Soltane & Longmin Wang, 2020. "Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 301-318, July.
    2. Amendola, Alessandra & Niglio, Marcella & Vitale, Cosimo, 2006. "The moments of SETARMA models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 625-633, March.
    3. Howell Tong & Iris Yeung, 1991. "On Tests for Self‐Exciting Threshold Autoregressive‐Type Non‐Linearity in Partially Observed Time Series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 43-62, March.
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