Long Memory Features in the Exchange Rates of Asia-pacific Countries

In this paper, we examine for long memory dynamics in the daily and weekly exchange rates of six Asia Pacific countries: Australia, Japan, New Zealand, Singapore, South Korea and Taiwan. Three semiparametric frequency domain estimators and the exact maximum likelihood estimator are used. Estimation results reveal strong evidence of long memory in the weekly exchange rate series for all six countries. On the other hand, we generally failed to detect long memory in the daily exchange rate series. The long memory estimates vary significantly across estimation procedures. The long memory estimates also vary significantly with the choice of frequency ordinates. Terence C. K. CHENG Department of Economics National University of Singapore CHAPTER ONE: INTRODUCTION Over the past two decades, numerous research have been directed towards understanding the stochastic process behind exchange rate dynamics. Exchange rate movements, like many economic and financial time series, have been empirically observed to exhibit large persistence and non-periodic yet mean-reverting cycles. The autoregressive integrated moving average (ARIMA) process has been the standard time series models to study exchange rates. The martingale, which is traditionally the most widely accepted model to represent exchange rate dynamics has important implications on forecasting, forward asset pricing, portfolio management and the efficiency of the currency markets. The development of the autoregressive fractionally integrated moving average (ARFIMA) process allows for a richer and more flexible class of time series models by extending the differencing process beyond the integer domain and permitting the order of integration parameter d to take any real, non-integer values. A stochastic process is fractionally integrated and said to contain long memory if longterm dependence exist between observations. From a statistical standpoint, long memory can be represented in terms of the degree of persistence in the observed autocorrelations from empirical data. The theoretical and empirical possibilities of the ARFIMA process have generated a vast amount of interest and research on its application to 1 A stochastic follows a “martingale” or “random walk” if it is well approximated by a first order, autoregressive process with a single unit root.