Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models
Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, 1353 Copenhagen K, Denmark
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Academic Editors: Katarina Juselius and Marc S. Paolella
Econometrics 2017, 5(3), 36; https://doi.org/10.3390/econometrics5030036
Received: 1 March 2017
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Revised: 15 August 2017
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Accepted: 17 August 2017
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Published: 22 August 2017
(This article belongs to the Special Issue Recent Developments in Cointegration)
A state space model with an unobserved multivariate random walk and a linear observation equation is studied. The purpose is to find out when the extracted trend cointegrates with its estimator, in the sense that a linear combination is asymptotically stationary. It is found that this result holds for the linear combination of the trend that appears in the observation equation. If identifying restrictions are imposed on either the trend or its coefficients in the linear observation equation, it is shown that there is cointegration between the identified trend and its estimator, if and only if the estimators of the coefficients in the observation equations are consistent at a faster rate than the square root of sample size. The same results are found if the observations from the state space model are analysed using a cointegrated vector autoregressive model. The findings are illustrated by a small simulation study.
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MDPI and ACS Style
Johansen, S.; Tabor, M.N. Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models. Econometrics 2017, 5, 36. https://doi.org/10.3390/econometrics5030036
AMA Style
Johansen S, Tabor MN. Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models. Econometrics. 2017; 5(3):36. https://doi.org/10.3390/econometrics5030036
Chicago/Turabian StyleJohansen, Søren, and Morten N. Tabor. 2017. "Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models" Econometrics 5, no. 3: 36. https://doi.org/10.3390/econometrics5030036
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