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

Anurag Banerjee (), Guillaume Chevillon () and Marie Kratz ()
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Marie Kratz: SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Asset Prices; Local Asymptotics; Random Coefficient Autoregressive Model; Bubbles (search for similar items in EconPapers)
Date: 2013-09-23
New Economics Papers: this item is included in nep-ets, nep-for and nep-ure
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