Chapter 2
Linear Time Series Analysis and Its Applications
In this chapter, we discuss basic theories of linear time series analysis, introduce some simple econometric models useful for analyzing financial data, and apply the models to financial time series such as asset returns. Discussions of the concepts are brief with emphasis on those relevant to financial applications. Understanding the simple time series models introduced here will go a long way to better appreciate the more sophisticated financial econometric models of the later chapters. There are many time series textbooks available. For basic concepts of linear time series analysis, see Box, Jenkins, and Reinsel (1994, Chapters 2 and 3) and Brockwell and Davis (1996, Chapters 1–3).
Treating an asset return (e.g., log return rt of a stock) as a collection of random variables over time, we have a time series {rt}. Linear time series analysis provides a natural framework to study the dynamic structure of such a series. The theories of linear time series discussed include stationarity, dynamic dependence, autocorrelation function, modeling, and forecasting. The econometric models introduced include (a) simple autoregressive (AR) models, (b) simple moving-average (MA) models, (b) mixed autoregressive moving-average (ARMA) models, (c) seasonal models, (d) unit-root nonstationarity, (e) regression models with time series errors, and (f) fractionally differenced models for long-range dependence. For an asset return rt, simple ...
