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A time-varying parameter model for local explosions

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  • Blasques, Francisco
  • Koopman, Siem Jan
  • Nientker, Marc

Abstract

Financial and economic time series can feature locally explosive behaviour when bubbles are formed. We develop a time-varying parameter model that is capable of describing this behaviour in time series data. Our proposed dynamic model can be used to predict the emergence, existence and burst of bubbles. We adopt a flexible observation driven model specification that allows for different bubble shapes and behaviour. We establish stationarity, ergodicity, and bounded moments of the data generated by our model. Furthermore, we obtain the consistency and asymptotic normality of the maximum likelihood estimator. Given the parameter estimates in the model, the implied filter is capable of extracting the unobserved bubble process from the observed data. We study finite-sample properties of our estimator through a Monte Carlo simulation study. Finally, we show that our model compares well with existing noncausal models in a financial application concerning the Bitcoin/US dollar exchange rate.

Suggested Citation

  • Blasques, Francisco & Koopman, Siem Jan & Nientker, Marc, 2022. "A time-varying parameter model for local explosions," Journal of Econometrics, Elsevier, vol. 227(1), pages 65-84.
    • Handle: RePEc:eee:econom:v:227:y:2022:i:1:p:65-84
    DOI: 10.1016/j.jeconom.2021.05.008
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    Cited by:

    1. Blasques, Francisco & Nientker, Marc, 2023. "Stochastic properties of nonlinear locally-nonstationary filters," Journal of Econometrics, Elsevier, vol. 235(2), pages 2082-2095.
    2. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    3. 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

    Speculative bubble; Explosive processes; Invertibility; Consistency; Asymptotic normality;
    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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