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Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model

Author

Listed:
  • Anurag Narayan Banerjee

    (Business school - Durham University)

  • Guillaume Chevillon

    (ESSEC Business School)

  • Marie Kratz

    (ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper proposes a Near Explosive Random-Coefficient autoregressive model for asset pricing which accommodates both the fundamental asset value and the recurrent presence of autonomous deviations or bubbles. Such a process can be stationary with or without fat tails, unit-root nonstationary or exhibit temporary exponential growth. We develop the asymptotic theory to analyze ordinary least-squares (OLS) estimation. One important theoretical observation is that the estimator distribution in the random coefficient model is qualitatively different from its distribution in the equivalent fixed coefficient model. We conduct recursive and full-sample inference by inverting the asymptotic distribution of the OLS test statistic, a common procedure in the presence of localizing parameters. This methodology allows to detect the presence of bubbles and establish probability statements on their apparition and devolution. We apply our methods to the study of the dynamics of the Case-Shiller index of U.S. house prices. Focusing in particular on the change in the price level, we provide an early detection device for turning points of booms and bust of the housing market.

Suggested Citation

  • Anurag Narayan Banerjee & Guillaume Chevillon & Marie Kratz, 2013. "Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model," Working Papers hal-00870795, HAL.
  • Handle: RePEc:hal:wpaper:hal-00870795
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-00870795
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    Cited by:

    1. Virtanen, Timo & Tölö, Eero & Virén, Matti & Taipalus, Katja, 2016. "Use of unit root methods in early warning of financial crises," Research Discussion Papers 27/2016, Bank of Finland.
    2. Virtanen, Timo & Tölö, Eero & Virén, Matti & Taipalus, Katja, 2017. "Use of unit root methods in early warning of financial crises," ESRB Working Paper Series 45, European Systemic Risk Board.
    3. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. repec:zbw:bofrdp:2016_027 is not listed on IDEAS
    5. Virtanen, Timo & Tölö, Eero & Virén, Matti & Taipalus, Katja, 2016. "Use of unit root methods in early warning of financial crises," Bank of Finland Research Discussion Papers 27/2016, Bank of Finland.
    6. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    7. Virtanen, Timo & Tölö, Eero & Virén, Matti & Taipalus, Katja, 2018. "Can bubble theory foresee banking crises?," Journal of Financial Stability, Elsevier, vol. 36(C), pages 66-81.

    More about this item

    Keywords

    Local Asymptotics; Asset Prices; Bubbles; Random Coefficient Autoregressive Model;
    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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