Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 61. Cointegration and Its Application in Finance

BALA ARSHANAPALLI, PhD

Professor of Finance, Indiana University Northwest

WILLIAM NELSON, PhD

Professor of Finance, Indiana University Northwest

Abstract: Financial time series data tend to exhibit stochastic trends. To uncover relationship among financial variables it is important to model changes in stochastic trends over time. Cointegration can be used to identify common stochastic trend among different financial variables. If financial variables are cointegrated, it can also be shown that the variables exhibit long-run relationship.

Keywords: deterministic trends, stationarity, unit root process, autoregression, cointegration, vector autoregressive model, error correction, Granger causality

The long-term relationships among economic variables, such as short-term versus long-term interest rates or stock prices versus dividends, have long interested finance practitioners. For certain types of trends, multiple regression analysis needs modification to uncover these relationships. A trend represents a long-term movement in the variable. One type of trend, a deterministic trend, has a straightforward solution. Since a deterministic trend is a function of time, we need merely include this time function in the regression. For example, if the variables are increasing or decreasing as a linear function of time, we may simply include time as a variable in the regression equation. The issue becomes more complex when the trend is stochastic. ...