Highest-density forecast regions: An essay in the Spanish stock market
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Natividad Blasco* received her PhD in Finance at the University of Zaragoza (Spain) and now she is a Professor of Financial Economics at the University of Zaragoza. Her major research interests are centred on the behaviour of stock prices (short-term and long-term memory, daily effects, non-linearities in the mean and in the variance, chaos theory). She has published in Applied Financial Economics, Journal of Business Finance and Accounting. International Journal of Finance, Applied Economics, Investigaciones Econo´micas, Revista Española de Financiacio´n y Contabilidad, Revista de Economı´a Aplicada, Informacio´n Comercial Española, etc.
Rafael Santamarı´a received his PhD in Finance at the University of Zaragoza (Spain). He has taught at the University of Zaragoza and the Public University of Navarra and now he is a Full Professor of Financial Economics at this University. His research interests include the behaviour of stock prices, foreign exchange, financial derivatives and asset pricing. He has published in Applied Economics Letters, Applied Financial Economics, International Journal of Finance, Journal of Business Finance and Accounting, Journal of Futures Markets, Applied Economics, Investigaciones Econo´micas, Revista Española de Financiacio´n y Contabilidad, Revista de Economı´a Aplicada, Informacio´n Comercial Española, etc. *Departmento de Gestio´n de Empresas, Universidad Pu´blica de Navarra, Campus de Arrosadı´a s/n, 31006 Pamplona, Spain. Tel:⫹34 948 169389; Fax: ⫹34 948 169404; E-mail: [email protected]
Abstract This paper explores the results of use of highest-density regions in practical forecasting. We study whether the information they provide is likely to be more effective compared with that offered by other easier methods of determining the forecast densities. Keywords: highest density regions; bootstrap techniques; conditional heteroscedasticity; January effect; day of the week effect
Introduction Under the conventional random walk model, it has been generally assumed that movements of stock prices are independent and identically distributed. Since the late 1980s, however, a series of papers have presented evidence of the potential short-horizon predictability (Lo and Mackinlay, 1988; French and Roll, 1986; Fama and French, 1988, and more recently Bremer et al., 1997; Huber, 1997; Grieb and Reyes, 1999, among others). These results provoke considerable research interest in other
274
Journal of Asset Management
types of models suggesting implied rejection of the traditional random walk hypothesis. Although the possibility of long-term memory in financial time series has also been studied in papers such as Mills (1993) and Cheung (1993), and more recently Berg and Lyhagen (1998), Lobato and Savin (1998) or Barkoulas et al. (2000), among others, there appears to be no conclusive empirical support for this alternative form of dependence. Particularly in the case of the Spanish stock market, Blasco and Santamarı´a (1996) do not find clear
Vol. 2, 3, 274–283
䉷 Henry Stewart Publications 14
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