Abstract
ARFIMA models generated an enormous amount of interest in the literature about three decades ago. However, this interest vaned after Granger (1999) showed that an ARFIMA process might have stochastic properties that do not mimic the properties of the data at all. The empirical results of our research in which we used exchange rate data for the analysis, show that a variant of an ARFIMA process indeed can beat the ARFIMA, the Random Walk and the ARMA process of the order one in out of sample forecasting. This indirectly indicates that our variant of the ARFIMA process can be considered as the data generating process for the long memory time series.
Highlights
The search for a model which can outperform random walk in out of sample forecasting was started about two decades ago in two important areas of study: volatility modelling and purchasing power parity (PPP) hypothesis
It has been recognized that the simple random walk can outperform many sophisticated volatility models in out of sample forecasting, while in purchasing power parity research, the existence of mean reverting behaviour in exchange rates has not been established convincingly yet
As the main objective of this paper is to prove that the YQ-ARFIMA model can beat the random walk model, we shall conduct this CM test only for the YQ-ARFIMA model versus the RW model for the selected 6 exchange rates for sample sizes 500, 1000, 2000, 5000 and at forecast horizons 5 periods, 20 periods, 60 periods and 240 periods
Summary
The search for a model which can outperform random walk in out of sample forecasting was started about two decades ago in two important areas of study: volatility modelling and purchasing power parity (PPP) hypothesis. It has been recognized that the simple random walk can outperform many sophisticated volatility models in out of sample forecasting, while in purchasing power parity research, the existence of mean reverting behaviour in exchange rates has not been established convincingly yet. In research on mean reversion behaviour, the most significant negative results were obtained by Meese and Rogoff (1983a, b) They evaluated the predictive ability of a series of linear structural exchange rate models and found that none was able to consistently outperform a simple random walk for all the known exchange rates and horizons. Recent work done by Taylor, Sarno, Clarida and Valente (2003) using nonlinear models show the promising positive result that there are structural models which can outperform random walk models in out of sample forecasting, or to put it differently, there is mean reverting behaviour in exchange rate
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