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Trend stationarity in the $$I(2)$$ cointegration model. (English) Zbl 1041.62522
Summary: A vector autoregressive model for $$I(2)$$ processes which allows for trend-stationary components and restricts the deterministic part of the process to be at most linear is defined. A two-step statistical analysis of the model is derived. The joint test of $$I(1)$$ and $$I(2)$$ cointegrating ranks is shown to be asymptotically similar with respect to the drift terms and the asymptotic distribution is tabulated. The cointegrating parameters are shown to be mixed Gaussian and an application for UK monetary data illustrates the proposed analysis.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
##### Keywords:
Similarity; Rank test; UK money demand
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##### References:
 [1] Chan, N. H.; Wei, C. Z.: Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of statistics 16, 367-401 (1988) · Zbl 0666.62019 [2] Haldrup, N.: The asymptotics of single-equation cointegration regressions with $$I(1)$$ and $$I(2)$$ variables. Journal of econometrics 63, 153-181 (1994) · Zbl 0814.62075 [3] Hansen, H.; Juselius, K.: CATS in ratscointegration analysis of time series. (1995) [4] Harbo, I., Johansen, S., Nielsen, B., Rahbek, A., 1995. Test for cointegrating rank in partial systems. Journal of Business and Economic Statistics, forthcoming. [5] Hendry, D. F.; Doornik, J. A.: Modelling linear dynamic econometric systems. Scottish journal of political economy 41, 1-33 (1994) [6] Hendry, D. F.; Ericsson, N. R.: Modelling the demand for narrow money in the united kingdom and the united states. European economic review 35, 833-881 (1991) [7] Hendry, D. F.; Mizon, G. E.: Evaluating dynamic econometric models by encompassing the VAR. Models, methods, and applications of econometrics (1993) [8] Johansen, S.: Statistical analysis of cointegration vectors. Journal of economic dynamics and control 12, 231-254 (1988) · Zbl 0647.62102 [9] Johansen, S.: Estimation and hypothesis testing of cointegration vectors in Gaussian vector autogressive models. Econometrica 59, 1551-1580 (1991) · Zbl 0755.62087 [10] Johansen, S.: Testing weak exogeneity and the order of cointegration in UK money demand. Journal of policy modeling 14, 313-334 (1992) [11] Johansen, S.: A representation of vector autoregressive processes integrated of order 2. Econometric theory 8, 188-202 (1992) [12] Johansen, S.: The role of the constant and linear terms in cointegration analysis of nonstationary variables. Econometric reviews 13, 205-229 (1994) · Zbl 0829.62086 [13] Johansen, S.: A statistical analysis of cointegration for $$I(2)$$ variables. Econometric theory 11, 25-59 (1995) · Zbl 1274.62597 [14] Johansen, S.: Identifying restrictions of linear equationswith applications to simultaneous equations and cointegration. Journal of econometrics 69, 111-132 (1995) · Zbl 0832.62100 [15] Johansen, S.: Likelihood-based inference in cointegrated vector autoregressive models. (1996) · Zbl 0928.62069 [16] Juselius, K.: On the duality between long-run relations and common trends in the $$I(1)$$ versus $$I(2)$$ modelan application to aggregate money holdings. Econometric reviews 13, 151-178 (1994) [17] Paruolo, P., 1995. Asymptotic efficiency of the two step estimator in I(2) systems. Econometric Theory, forthcoming. · Zbl 1009.62079 [18] Paruolo, P.: On the determination of integration indices in $$I(2)$$ systems. Journal of econometrics 72, 313-356 (1996) · Zbl 0844.62096 [19] Phillips, P. C. B.: Optimal inference in cointegrated systems. Econometrica 59, 283-306 (1991) · Zbl 0729.62104 [20] Rahbek, A., 1997. Representation of cointegrated I(2) and I(1) processes with deterministic trends. Manuscript, Department of Theoretical Statistics, University of Copenhagen.
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