Fractional ARIMA processes and applications in modeling financial time series

Abstract

Time-series analysis is widely used in forecasting future trends on financial markets. There is a family of models which represent the property of long memory. In this thesis we aim at introducing fractionally differentiated ARIMA model in forecasting future returns of market index. In theoretical part the description of long-memory processes and statistical testing of given data are provided. In practical part we fit the models without differencing, with differencing and with fractional differencing to the market data and compare its forecast accuracy with observed values.