Probability and Statistics for Finance

Chapter 7. Introduction to Time Series Analysis

In this chapter, we introduce the element of time as an index of a series of univariate observations. Thus, we treat observations as being obtained successively rather than simultaneously. We present a simple time series model and its components. In particular, we focus on the trend, the cyclical, and seasonal terms as well as the error or disturbance of the model. Furthermore, we introduce the random walk and error correction models as candidates for modeling security price movements. Here the notion of innovation appears. Time series are significant in modeling price processes as well as the dynamics of economic quantities.

WHAT IS TIME SERIES?

So far, we have either considered two-component variables cross-sectionally coequal, which was the case in correlation analysis, or we have considered one variable to be, at least partially, the functional result of some other quantity. The intent of this section is to analyze variables that change in time, in other words, the objects of the analysis are time series. The observations are conceived as compositions of functions of time and other exogenous and endogenous variables as well as lagged values of the series itself or other quantities. These latter quantities may be given exogenously or also depend on time.

To visualize this, we plot the graph of 20 daily closing values of the German stock market index, the DAX, in Figure 7.1. The values are listed in Table 7.1. The time points of observation ...