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A nonlinear threshold model for the dependence of extremes of stationary sequences

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  • Martínez Ibáñez, Oscar
  • Olmo, José

Abstract

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

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Bibliographic Info

Paper provided by Universitat Rovira i Virgili, Department of Economics in its series Working Papers with number 2072/5361.

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Date of creation: 2008
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Handle: RePEc:urv:wpaper:2072/5361

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Related research

Keywords: Crisis financeres; Observacions aberrants (Estadística); Hipòtesi estadística -- Proves; Teories no-lineals; 519.1 - Teoria general de l'anàlisi combinatòria. Teoria de grafs;

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  1. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
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  13. Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "On the Exact Moments of Asymptotic Distributions in an Unstable AR(1) with Dependent Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 71-88, February.
  14. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207, Octomber.
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