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Hidden Threshold Models with applications to asymmetric cycles

Author

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  • Harvey, A.
  • Simons, J.

Abstract

Threshold models are set up so that there is a switch between regimes for the parameters of an unobserved components model. When Gaussianity is assumed, the model is handled by the Kalman filter. The switching depends on a component crossing a boundary, and, because the component is not observed directly, the error in its estimation leads naturally to a smooth transition mechanism. A prominent example motivating thresholds is that of a cyclical time series characterized by a downturn that is more, or less, rapid than the upturn. The situation is illustrated by fitting a model with three potentially asymmetric cycles, each with its own threshold, to observations on ice volume in Antarctica since 799,000 BCE. The model is able to produce multi-step forecasts with associated prediction intervals. A second example shows how a hidden threshold model is able to deal with the asymmetric cycle in monthly US unemployment.

Suggested Citation

  • Harvey, A. & Simons, J., 2024. "Hidden Threshold Models with applications to asymmetric cycles," Cambridge Working Papers in Economics 2448, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2448
    Note: ach34, jrs89
    as

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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Conditionally Gaussian state space model; Kalman filter; nonlinear time series model; regimes; smooth transition autoregressive model; unobserved components;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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