Abstract
Suppose one could find a stock whose price (or log-price) series was stationary and therefore mean-reverting. This would be a wonderful investment opportunity. Whenever the price was below the mean, one could buy the stock and realize a profit when the price returned to the mean. Similarly, one could realize profits by selling short whenever the price was above the mean. Alas, returns are stationary but not prices. We have seen that log-prices are integrated. However, not all is lost. Sometimes one can find two or more assets with prices so closely connected that a linear combination of their prices is stationary. Then, a portfolio with weights assigned by the cointegrating vector, which is the vector of coefficients of this linear combination, will have a stationary price. Cointegration analysis is a means for finding cointegration vectors.
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Ruppert, D., Matteson, D.S. (2015). Cointegration. In: Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2614-5_15
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DOI: https://doi.org/10.1007/978-1-4939-2614-5_15
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