Modeling Volatility using ARCH and GARCH Processes

Abstract

[en] The main goal of this thesis is to present ARCH and GARCH models, key concepts in Time Series Analysis. These models are extremely useful when describing the behavior of Financial time series (i.e. Stock returns, Exchange rates, Economic indexs...), because they deal with volatility (variation of price in a delimited time period). The discipline of Time Series Analysis as a whole is introduced, as well as its main concepts, which are needed to further explore the useful properties behind ARCH and GARCH. We put special emphasis in developing a consistent theory of Estimation and Forecasting (i.e determinate the parameters of a model and predict future values) for Time Series Analysis, which serves as a justification for estimating and predicting ARCH and GARCH models. Practical examples are given using the R statistics package.