An Introduction to Analysis of Financial Data with R

In this chapter, we discuss the methods and linear models useful in modeling and forecasting financial time series. We use real examples to introduce important statistical concepts, illustrate step-by-step data analysis, and discuss financial applications. For general concepts of linear time series analysis, see Tsay (2010, Chapter 2), Box et al. (1994, Chapters 2 and 3), Brockwell and Davis (2002, Chapters 1–3), Shumway and Stoffer (2000), and Woodward et al. (2012).

The models introduced include (i) simple autoregressive (AR) models, (ii) simple moving average (MA) models, (iii) mixed autoregressive moving average (ARMA) models, (iv) unit-root models including unit-root tests, (v) exponential smoothing, (vi) seasonal models, (vii) regression models with time series errors, and (viii) fractionally differenced models for long-range dependence. For each class of models, we study their fundamental properties, introduce methods for model selection, consider ways to produce prediction, and discuss their applications. The chapter also discusses methods for comparing different models, for example, backtesting and model averaging in prediction.

Let {x_t} be a collection of certain financial measurements over time. Figure 2.1 shows the daily closing price of Apple stock from January 3, 2003 to April 5, 2010. The daily prices exhibit certain degrees of variability and show an upward movement ...