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Journal of Financial Econometrics Advance Access originally published online on March 1, 2007
Journal of Financial Econometrics 2007 5(2):266-284; doi:10.1093/jjfinec/nbm002
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Copyright © The Author 2007. Published by Oxford University Press.

A discrete and a continuous-time model based on a technical trading rule

João Nicolau
     School of Economics and Management (ISEG)–Technical University of Lisbon (UTL)

Address correspondence to João Nicolau, ISEG, Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal, or e-mail: nicolau{at}iseg.utl.pt


  Abstract

In this article we propose a model in discrete and continuous time that incorporates explicitly a technical trading rule in the specification of the volatility. The proposed discrete-time model is an alternative to GARCH-type processes. We derive conditions for the covariance and strict stationarity of the discrete-time process and we study the estimation and inference problems. We also analyze the conditions under which the discrete-time process converges in distribution to a diffusion process. To illustrate the proposed model and compare it with the GARCH specification, we analyze the daily closing stock prices of two major U.S. companies (Microsoft and Oracle), two stock indices (DAX and NASDAQ) and two U.S. Dollar exchange rates (Euro and Sterling)

KEYWORDS: conditional heteroskedasticity, parametric estimation, stochastic differential equations, diffusion processes

I am grateful to the Editor Eric Renault and two referees for their helpful comments and for correcting some of my errors, and Tom Kundert for his assistance in revising this version. This research was supported by the Fundação para a Ciência e a Tecnologia (FCT) and by FEDER/POCI 2010.

Received April 10, 2006; revised November 7, 2006; accepted January 19, 2007


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