Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Cointegration between Trends and Their Estimators in State Space Models and Cointegrated Vector Autoregressive Models. / Johansen, Søren; Tabor, Morten Nyboe.
In: Econometrics, Vol. 5, No. 3, 22.08.2017, p. 1-15.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
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 - 2017/8/22
Y1 - 2017/8/22
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
VL - 5
SP - 1
EP - 15
JO - Econometrics
JF - Econometrics
SN - 2225-1146
IS - 3
ER -
ID: 193398888