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英文文献：Cointegration between trends and their estimators in state space models and CVAR models
英文文献作者：S?ren Johansen,Morten Nyboe Tabor
英文文献摘要：
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.
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