Cointegration between trends and their estimators in state space models and CVAR models

Søren Johansen, Morten Nyboe Tabor

Publikation: Working paper/Preprint Working paperForskning

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In a linear state space model, y_{t+1}=BT_{t}+eps_{t+1}, we investigate if the unobserved trend, T_{t}, cointegrates with the extracted trend E_{t}T_{t}, and with the estimated trend E^_{t}T_{t}, in the sense that the spreads T_{t}-E_{t}T_{t} and E_{t}T_{t}-E^_{t}T_{t} are stationary. We find that this result holds for BT_{t}-BE_{t}T_{t} and BE_{t}T_{t}-B^E^_{t}T_{t}. For the trends T_{t} and E^_{t}T_{t}, however, this type cointegration depends on the identification of B and T_{t}. 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 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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider13
StatusUdgivet - 2017
NavnCREATES Research Paper


  • Cointegration of trends, State space models, CVAR models