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A note on the consistency of a robust estimator for threshold autoregressive processes

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  • Zhang, Li-Xin
  • Chan, Wai-Sum
  • Cheung, Siu-Hung
  • Hung, King-Chi

Abstract

The method of conditional least squares is commonly used for estimating threshold autoregressive parameters, and its consistency was derived by Chan [Chan, K.S., 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Annals of Statistics 21, 520-533]. In this note we consider a general class of robust estimators for threshold autoregressive models, and under some regularity conditions and a proper choice of the weight function, the consistency is demonstrated.

Suggested Citation

  • Zhang, Li-Xin & Chan, Wai-Sum & Cheung, Siu-Hung & Hung, King-Chi, 2009. "A note on the consistency of a robust estimator for threshold autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 807-813, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:807-813
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    References listed on IDEAS

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    1. Kapetanios, George, 2000. "Small sample properties of the conditional least squares estimator in SETAR models," Economics Letters, Elsevier, vol. 69(3), pages 267-276, December.
    2. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, September.
    3. Paolo Giordani, 2006. "A cautionary note on outlier robust estimation of threshold models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 37-47.
    4. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
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    Cited by:

    1. Chan Wai-Sum & Hung King-Chi, 2011. "On Robust Testing and Modelling of Threshold-Type Non-Linearity in ASEAN Foreign Exchange Markets," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 5(2), pages 1-16, July.
    2. Grossi, Luigi & Nan, Fany, 2019. "Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources," Technological Forecasting and Social Change, Elsevier, vol. 141(C), pages 305-318.
    3. Luigi Grossi & Fany Nan, 2017. "Forecasting electricity prices through robust nonlinear models," Working Papers 06/2017, University of Verona, Department of Economics.
    4. Luigi Grossi & Fany Nan, 2018. "The influence of renewables on electricity price forecasting: a robust approach," Working Papers 2018/10, Institut d'Economia de Barcelona (IEB).

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