Conditional heteroskedasticity : some results on estimation, inference and signal extraction, with an application to seasonal adjustment

Abstract

This thesis is about economic time series analysis and econometrics. It centers around the use of Autoregressive Conditional Heteroskedasticity models (Arch), even though Arch models are not the only subject of the thesis. They are also used as a playground on which to exercise those aspects of econometrics which are considered in the thesis, such as seasonal adjustment, filtering, computational methods and inference with quasi maximum likelihood estimators. I begin by introducing time series analysis with Autoregressive Integrated Moving Average (Arima) and Arch models. This introduction is intended to define notation; the mathematical operators; and the basic properties of the models to be used in subsequent chapters rather than to be a survey on time series analysis find Arch models. Some of the issues to be addressed in the remaining chapters will also be introduced when needed. A unified treatment of most of the concepts introduced in this chapter can be found in the books of Box and Jenkins (1970), Granger and Newbold (1986), Harvey (1981), Piccolo (1990) and Priestley (1981).