Abstract
The regression theory of Chapter 6 and the VAR models discussed in the previous chapter are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory often implies equilibrium relationships between the levels of time series variables that are best described as being I(1). Similarly, arbitrage arguments imply that the I(1) prices of certain financial time series are linked. This chapter introduces the statistical concept of cointegration that is required to make sense of regression models and VAR models with I(1) data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
12.7 References
Alexander, C. (2001). Market Models: A Guide to Financial Data Analysis, John Wiley & Sons, Chichester, UK.
Cochrane, J. (2001). Asset Pricing. Princeton University Press, Princeton, NJ.
Engle, R.F. and C.W.J. Granger (1987). “Co-Integration and Error Correction: Representation, Estimation and Testing,” Econometrica, 55, 251–276.
Granger, C.W.J. and P.E. Newbold (1974). “Spurious Regression in Econometrics,” Journal of Econometrics, 2, 111–120.
Hamilton, J.D. (1994). Time Series Analysis, Princeton Unversity Press, Princeton, NJ.
Hansen, B.E. (1992). “Efficient Estimation and Testing of Cointegrating Vectors in the Presence of Deterministic Trends,” Journal of Econometrics, 53, 87–121.
Hayashi, F. (2000). Econometrics, Princeton University Press, Princeton, NJ.
Johansen, S. (1988). “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, 12, 231–254.
Johansen, S. (1995). Likelihood Based Inference in Cointegrated Vector Error Correction Models, Oxford University Press, Oxford.
MacKinnon, J. (1996). “Numerical Distribution Functions for Unit Root and Cointegration Tests,” Journal of Applied Econometrics, 11, 601–618.
Mills, T. (1999). The Econometric Analysis of Financial Time Series, Cambridge University Press, Cambridge.
Osterwald-Lenum, M. (1992). “A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Statistics,” Oxford Bulletin of Economics and Statistics, 54, 461–472.
Phillips, P.C.B. (1986). “Understanding Spurious Regression in Econometrics,” Journal of Econometrics, 33, 311–340.
Phillips, P.C.B. (1991). “Optimal Inference in Cointegrated Systems,” Econometrica, 59, 283–306.
Phillips, P.C.B. and S. Ouliaris (1990). “Asymptotic Properties of Residual Based Tests for Cointegration,” Econometrica, 58, 73–93.
Reimars, H.-E. (1992). “Comparisons of Tests for Multivariate Cointegration,” Statistical Papers, 33, 335–359.
Reinsel, G.C. and S.K. Ahn (1992). “Vector Autoregression Models with Unit Roots and Reduced Rank Structure: Estimation, Likelihood Ratio Test, and Forecasting,” Journal of Time Series Analysis, 13, 353–375.
Sims, C.A., J.H. Stock and M.W. Watson (1990). “Inference in Linear Time Series Models with Some Unit Roots,” Econometrica, 58, 113–144.
Stock, J.H. (1987). “Asymptotic Properties of Least Squares Estimation of Cointegrating Vectors,” Econometrica, 55, 1035–1056.
Stock, J.H. and M.W. Watson (1989). “Variable Trends in Economic Time Series,” Journal of Economic Perspectives, Vol. 2(3), 147–174.
Stock, J.H. and M.W. Watson (1993). “A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems,” Econometrica, 61, 783–820.
Tsay, R. (2001). The Analysis of Financial Time Series, John Wiley & Sons, New York.
Zivot, E. (2000). “Cointegration and Forward and Spot Exchange Rate Regressions,” Journal of International Money and Finance, 19, 785–812.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
(2006). Cointegration. In: Modeling Financial Time Series with S-PLUS®. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32348-0_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-32348-0_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-27965-7
Online ISBN: 978-0-387-32348-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)