This dissertation provides a survey and review of the major models that help us analyze volatility, stochastic volatility, long memory stochastic volatility and fractional differencing. We also make a review on AR, MA, ARMA, ARIMA and ARFIMA models and other tools such as spectrum density that are needed to analyze the above. In section 4 we will show how the fractional differencing is connected with parameter d and long-term memory. Section 5 presents the empirical analysis, which shows whether long memory appears in the U.S.A. market and in particular in the S&P500, Dow Jones, Nasdaq and Russell 2000 indices. Furthermore, we see the volatility which was created by the Dot-com bubble and the financial crisis that have occurred in America and affected these four indices.
(EN)
University of Ioannina
