Cointegration Between Trends and Their Estimators in State Space Models and CVAR Models

13 Pages Posted: 15 Mar 2017

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Morten Tabor

University of Copenhagen - Department of Economics

Date Written: March 14, 2017

Abstract

In a linear state space model Y(t)=BT(t) e(t), we investigate if the unobserved trend, T(t), cointegrates with the predicted trend, E(t), and with the estimated predicted trend, in the sense that the spreads are stationary. We find that this result holds for the spread B(T(t)-E(t)) and the estimated spread. For the spread between the trend and the estimated trend, T(t)-E(t), however, cointegration depends on the identification of B. The same results are found, if the observations Y(t), from the state space model are analysed using a cointegrated vector autoregressive model, where the trend is defined as the common trend. Finally, we investigate cointegration between the spread between trends and their estimators based on the two models, and find the same results. We illustrate with two examples and confirm the results by a small simulation study.

Keywords: Cointegration of trends, State space models, CVAR models

JEL Classification: C32

Suggested Citation

Johansen, Soren and Tabor, Morten, Cointegration Between Trends and Their Estimators in State Space Models and CVAR Models (March 14, 2017). Available at SSRN: https://ssrn.com/abstract=2932853 or http://dx.doi.org/10.2139/ssrn.2932853

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Morten Tabor

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

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