Portuguese Stock Market: A Long-Memory Process?

Abstract

Abstract. This paper gives a basic overview of the various attempts at modelling stochastic processes for stock markets with a specific application to the Portuguese stock market data. Long-memory dependence in the stock prices would completely alter the data generation process and econometric models not considering the long-range dependence would exhibit poor forecasting abilities. The Hurst exponent is used to identify the presence of long-memory or fractal behaviour of the data generation process for the daily returns to ascertain if the process follows a fractional brownian motion. Detrended fluctuation analysis (DFA) using linear and quadratic trends and the Geweke Porter-Hudak methods are applied to detect the presence of long-memory or persistence. We find that the daily returns exhibit a small amount of long memory and that the quadratic trend used in the DFA overestimates the value of the Hurst exponent. These findings are corroborated by the use of the Geweke Porter-Hudak method wherein the Hurst exponent is close to the DFA using the linear trend. Keywords

The Efficient Market Hypothesis: Empirical Evidence

“…Their broad conclusion was that there is no long memory in the return series of the Korean stock market. Rege and Martín (2011) calculated the Hurst exponent for the Portuguese stock market and concluded that it exhibits both long memory and short memory depending on the scale of the time period used. Mishra et al (2011) used R/S analysis on daily returns from the Indian stock market to reveal strong evidence of persistence or temporal dependencies.…”