Chapter Preview. This chapter begins our study of time series data by introducing techniques to account for major patterns, or trends, in data that evolve over time. The focus is on how regression techniques developed in earlier chapters can be used to model trends. Further, new techniques, such differencing data, allow us to naturally introduce a random walk, an important model of efficient financial markets.

Introduction

Time Series and Stochastic Processes

Business firms are not defined by physical structures such as the solid stone bank building that symbolizes financial security. Nor are businesses defined by spacealien invader toys that they manufacture for children. Businesses comprise several complex, interrelated processes. A process is a series of actions or operations that lead to a particular end.

Processes not only are the building blocks of businesses but also provide the foundations for our everyday lives. We may go to work or school every day, practice martial arts, or study statistics. These are regular sequences of activities that define us. In this text, our interest is in modeling stochastic processes, defined as ordered collections of random variables that quantify a process of interest.

Some processes evolve over time, such as daily trips to work or school, or the quarterly earnings of a firm. We use the term longitudinal data for measurements of a process that evolves over time.