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Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour

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Abstract

This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S\&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.

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  • Yubo Tao & Peter C.B. Phillips & Jun Yu, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Cowles Foundation Discussion Papers 2114, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2114
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    Cited by:

    1. Lieberman, Offer & Phillips, Peter C.B., 2022. "Understanding temporal aggregation effects on kurtosis in financial indices," Journal of Econometrics, Elsevier, vol. 227(1), pages 25-46.
    2. Yang, Bingduo & Long, Wei & Yang, Zihui, 2022. "Testing predictability of stock returns under possible bubbles," Journal of Empirical Finance, Elsevier, vol. 68(C), pages 246-260.
    3. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    4. Nishi, Mikihito & 西, 幹仁 & Kurozumi, Eiji & 黒住, 英司, 2022. "Stochastic Local and Moderate Departures from a Unit Root and Its Application to Unit Root Testing," Discussion Papers 2022-02, Graduate School of Economics, Hitotsubashi University.
    5. Offer Lieberman & Peter C.B. Phillips, 2017. "Latent Variable Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 3013, Cowles Foundation for Research in Economics, Yale University.
    6. Liu, Yanbo & Phillips, Peter C.B., 2023. "Robust inference with stochastic local unit root regressors in predictive regressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 563-591.
    7. Shuping Shi & Jun Yu, 2023. "Volatility Puzzle: Long Memory or Antipersistency," Management Science, INFORMS, vol. 69(7), pages 3861-3883, July.
    8. Xuanling Yang & Dong Li & Ting Zhang, 2024. "A simple stochastic nonlinear AR model with application to bubble," Papers 2401.07038, arXiv.org.

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    More about this item

    Keywords

    Continuous time models; Explosive path; Extreme behaviour; Random coefficient autoregression; Infill asymptotics; Bubble testing;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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