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

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  • rp17_11

    Final published version, 368 KB, PDF-document

  • Søren Johansen
  • Morten Nyboe Tabor
    Morten Nyboe TaborUniversity of CopenhagenDenmark
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.
Original languageDanish
Place of PublicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages13
StatePublished - 2017
SeriesCREATES Research Papers
Number2017-11

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