Abstract
This chapter is addressed to the analysis of cointegrated variables. Properties like superconsistency of the LS estimator and conditions for asymptotic normality are extensively discussed. Error-correction is the reverse of cointegration, which is why we provide an introduction to the analysis of error-correction models as well. In particular, we discuss cointegration testing. In 2003, Clive W.J. Granger was awarded the Nobel prize for introducing the concept of cointegration. Finally, we stress once more the effect of linear time trends underlying the series.
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Banerjee, A., Dolado, J. J., & Mestre R. (1998). Error-correction mechanism tests for cointegration in a single-equation framework. Journal of Time Series Analysis, 19, 267–283.
Boswijk, H. P. (1994). Testing for an unstable root in conditional and structural error correction models. Journal of Econometrics, 63, 37–60.
Davidson, J., Hendry, D. F., Srba, F., & Yeo S. (1978). Econometric modelling of the aggregate time-series relationship between consumers’ expenditure and income in the United Kingdom. Economic Journal, 88, 661–692.
Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55, 251–276.
Ericsson, N. R., & MacKinnon, J. G. (2002). Distributions of error correction tests for cointegration. Econometrics Journal, 5, 285–318.
Frisch, R., & Waugh, F. V. (1933). Partial time regressions as compared with individual trends. Econometrica, 1, 387–401.
Hamilton, J. (1994). Time series analysis. Princeton: Princeton University Press.
Hansen, B. E. (1992). Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends. Journal of Econometrics, 53, 87–121.
Harris, D., & Inder, B. (1994). A test of the null hypothesis of cointegration. In C. P. Hargreaves (Ed.), Nonstationary time series analysis and cointegration (pp. 133–152). Oxford/New York: Oxford University Press.
Hassler, U. (2000a). Cointegration testing in single error-correction equations in the presence of linear time trends. Oxford Bulletin of Economics and Statistics, 62, 621–632.
Hassler, U. (2000b). The KPSS test for cointegration in case of bivariate regressions with linear trends. Econometric Theory, 16, 451–453.
Hassler, U. (2001). The effect of linear time trends on the KPSS test for cointegration. Journal of Time Series Analysis, 22, 283–292.
Johansen, S. (1995). Likelihood-based inference in cointegrated vector autoregressive models. Oxford/New York: Oxford University Press.
Krämer, W. (1986). Least squares regression when the independent variable follows an ARIMA process. Journal of the American Statistical Association, 81, 150–154.
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178.
Leybourne, S. J., & McCabe, B. P. M. (1994). A simple test for cointegration. Oxford Bulletin of Economics and Statistics, 56, 97–103.
MacKinnon, J. G. (1991). Critical values for co-integration tests. In R. F. Engle, & C. W. J. Granger (Eds.), Long-run economic relationships (pp. 267–276). Oxford/New York: Oxford University Press.
MacKinnon, J. G. (1996). Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics, 11, 601–618.
Park, J. Y. (1992). Canonical cointegrating regressions. Econometrica, 60, 119–143.
Phillips, P. C. B. (1986). Understanding spurious regressions in econometrics. Journal of Econometrics, 33, 311–340.
Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica, 55, 277–301.
Phillips, P. C. B. (1991). Optimal inference in cointegrated systems. Econometrica, 59, 283–306.
Phillips, P. C. B., & Durlauf, S. N. (1986). Multiple time series regression with integrated processes. Review of Economic Studies, LIII, 473–495.
Phillips, P. C. B., & Hansen, B. E. (1990). Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies, 57, 99–125.
Phillips, P. C. B., & Loretan, M. (1991). Estimating long-run economic equilibria. Review of Economic Studies, 58, 407–436.
Phillips, P. C. B., & Ouliaris, S. (1990). Asymptotic properties of residual based tests for cointegration. Econometrica, 58, 165–193.
Phillips, P. C. B., & Park, J. Y. (1988). Asymptotic equivalence of ordinary least squares and generalized least squares in regressions with integrated regressors. Journal of the American Statistical Association, 83, 111–115.
Saikkonen, P. (1991). Asymptotically efficient estimation of cointegration regressions. Econometric Theory, 7, 1–21.
Shin, Y. (1994). A residual-based test of the Null of cointegration against the alternative of no cointegration. Econometric Theory, 10, 91–115.
Stock, J. H. (1987). Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica, 55, 1035–1056.
Stock, J. H., & Watson, M. W. (1993). A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica, 61, 783–820.
West, K. D. (1988). Asymptotic normality, when regressors have a unit root. Econometrica, 56, 1397–1418.
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Hassler, U. (2016). Cointegration Analysis. In: Stochastic Processes and Calculus. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-23428-1_16
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