Aplikacja modeli klasy ARCH do estymacji parametru beta przy uwzględnieniu stóp zwrotu dla różnych interwałów czasowych - Brzeszczyński, Janusz; Gajdka, Jerzy; Schabek, Tomasz (Application of ARCH Models for the Estimation of Beta Parameters Using Different Time Intervals for Returns, 2008)
The estimation of beta coefficient (ß), a basic measure of systematic risk, is central to the implementation of the capital assets pricing model (CAPM) and is of great importance from both theoretical and practical viewpoints. The most frequently used tool for estimation of the ß parameter is a regression model and the ordinary least squares method (OLS). Its application is justified, however, only when all standard assumptions of the OLS are fulfilled, including the assumption about homoscedasticity of the variance of an error term. The consequences of using the OLS under the existence of heteroscedacity can be serious and usually lead to obtaining incorrect estimates of the model's parameters, which may result in the formulation of wrong conclusions about the analyzed relationships. This paper presents empirical results from the estimation of the ß parameters for stocks listed on the Warsaw Stock Exchange (WSE) between 2003 and 2006 using the OLS and ARCH models as well as different intervals over which the returns have been measured. Our findings provide evidence that those estimates considerably differ with the intervals length. They indicate also that in the sample of data the estimates of ß increased as the returns interval was lengthened and that the application of the OLS, whenever heteroscedasticity was present, usually resulted in overestimation of beta coefficients
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2008; nr 1200, s. 69-76