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Encyclopedia of Financial Models, 3 Volume Set by Frank J. Fabozzi

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Applying Cointegration to Problems 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 relationships among financial variables it is important to model changes in stochastic trends over time. Cointegration can be used to identify common stochastic trends among different financial variables. If financial variables are cointegrated, it can also be shown that the variables exhibit a long-run relationship. If this long-run relationship is severed, this may indicate the presence of a financial bubble.

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 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. A stochastic trend is defined (Stock and Watson, 2003) as “a ...

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