Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models

TY - JOUR

T1 - Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models

AU - Johansen, Søren

AU - Tabor, Morten Nyboe

PY - 2017/9

Y1 - 2017/9

N2 - 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.

AB - 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.

KW - Faculty of Social Sciences

KW - cointegration of trends

KW - state space models

KW - cointegrated vector autoregressive models

U2 - 10.3390/econometrics5030036

DO - 10.3390/econometrics5030036

M3 - Journal article

SN - 2225-1146

VL - 5

SP - 1

EP - 15

JO - Econometrics

JF - Econometrics

IS - 3

ER -