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Maximum likelihood estimation of a generalized threshold stochastic regression model

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  • Noelle I. Samia
  • Kung-Sik Chan

Abstract

There is hardly any literature on modelling nonlinear dynamic relations involving nonnormal time series data. This is a serious lacuna because nonnormal data are far more abundant than normal ones, for example, time series of counts and positive time series. While there are various forms of nonlinearities, the class of piecewise-linear models is particularly appealing for its relative ease of tractability and interpretation. We propose to study the generalized threshold model which specifies that the conditional probability distribution of the response variable belongs to an exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. We introduce a likelihood-based estimation scheme, and the consistency and limiting distribution of the maximum likelihood estimator are derived. We illustrate the proposed approach with an analysis of a hare abundance time series, which gives new insights on how phase-dependent predator-prey-climate interactions shaped the ten-year hare population cycle. A simulation study is conducted to examine the finite-sample performance of the proposed estimation method. Copyright 2011, Oxford University Press.

Suggested Citation

  • Noelle I. Samia & Kung-Sik Chan, 2011. "Maximum likelihood estimation of a generalized threshold stochastic regression model," Biometrika, Biometrika Trust, vol. 98(2), pages 433-448.
  • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:433-448
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    File URL: http://hdl.handle.net/10.1093/biomet/asr008
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    Cited by:

    1. Wu, K.Y.K. & Li, W.K., 2015. "Double Generalized Threshold Models with constraint on the dispersion by the mean," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 59-73.
    2. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    3. Dimitris Christopoulos & Peter McAdam & Elias Tzavalis, 2023. "Exploring Okun's law asymmetry: An endogenous threshold logistic smooth transition regression approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(1), pages 123-158, February.
    4. Tong, Howell, 2015. "Threshold models in time series analysis—Some reflections," Journal of Econometrics, Elsevier, vol. 189(2), pages 485-491.
    5. N. R. Ramírez-Rondán, 2020. "Maximum likelihood estimation of dynamic panel threshold models," Econometric Reviews, Taylor & Francis Journals, vol. 39(3), pages 260-276, March.
    6. Thomas Kopp, 2022. "When switching costs cause market power: Rubber processing in Indonesia," Agricultural Economics, International Association of Agricultural Economists, vol. 53(3), pages 481-495, May.
    7. Andrew Hodge & Sriram Shankar, 2016. "Single-Variable Threshold Effects in Ordered Response Models With an Application to Estimating the Income-Happiness Gradient," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 42-52, January.

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