Models for long-memory and high-frequency financial time series

This dissertation is composed of five distinct chapters, all of which model and examine the long memory properties in different financial time series data.; Chapter 2 considers the use of a long memory volatility process, FIGARCH, in representing Deutsche Mark - US {dollar} spot exchange rate returns for both high and low frequency returns data. The Flexible Fourier Form (FFF) filter and a FIGARCH type model is used to represent the volatility process.; Chapter 3 is concerned with the econometric modeling and appropriate specification of models to describe exchange rates in a target zone. A long memory GARCH model with a jump process generated by either a Bernoulli or Poisson process is used for the daily FF-DM returns data.; Chapter 4 examines one of the earliest recorded periods of central bank intervention in the 1920s foreign exchange market. A relatively new set of daily data for four currencies is examined and returns are found to be close to martingales with unusually persistent volatility processes, which are represented by FIGARCH models. The effect of intervention by the French government to support the French franc is represented by dynamic dummy variables. There is strong evidence that the intervention was successful for about six months before the FF again depreciated. In contrast, the corresponding effects of the intervention on the conditional variance seem to be insignificant. The intervention was not associated with increasing the volatility of the currencies. Hence, the overall conclusion appears to be that the intervention was successful in the short run, but was unable to prevent substantial depreciation over a six month horizon.; Chapter 5 is concerned with modeling inflation for nine countries. The inflation series appear to have dual long memory features in both their first and second conditional moments. This chapter implements a combined ARFIMA-FIGARCH model to represent the inflation series. For nearly all of the countries, there is strong evidence of long memory features in both the conditional mean and variance.; Chapter 6 is concerned with the bivariate relationship between high frequency time series for the DM-{dollar} spot exchange rate and the corresponding US and German 30 day Eurobond interest rate differential. The well known forward premium anomaly critically depends on the order of integration of the interest rate differential, i.e. forward premium. The use of parametric ARFIMA-FIGARCH models and also semi parametric local Whittle estimation methods is to estimate the order of fractional integration. The high frequency forward premium is found to have finite cumulative impulse response weights, but to be non stationary and to have very persistent autocorrelations. This chapter concludes with a brief discussion of the implications of the results for the resolution of the forward premium anomaly.