Essays on financial time series models : Stochastic volatility and long memory

Abstract: This work consists of five articles about the statistical aspects of financial time series models. The first three papers investigate and develop the inverse normal Gaussian stochastic volatility (NIGSV) model, initially suggested by Barndorff- Nielsen (1997). In the first paper, Barndorff-Nilsen's model is generalized in order to be able to produce a more flexible lag structure. The moments of the squared process, important properties of volatility models, are derived. The topic of the second paper is the performance of the maximum likelihood estimator of the NIGSV model. In the third paper a comparison of the NIGSV model with two other commonly used volatility models is made.The long memory property is the topic of the last two papers. In the fourth paper two improvements of the commonly used GPH-estimator of Geweke and Porter-Hudak (1983) are proposed and studied by means of a Monte Carlo study. In the fifth paper the problem of distinguishing between short term and long term memory in volatilityis investigated.