Observation Driven Long Run Equilibria

In this paper the Fractional Vector Error Correction Model (FVECM) is extended by allowing three of its parameters to vary with time: the equilibrium relationship parameter β, the variance σ² and the cointegration degree parameter b. These parameters are independently updated based on the Generalized Autoregressive Score (GAS) framework. In this way three new FVECM–GAS models are created, and also the concept of ‘time-varying cointegration’ is introduced. Data from these models are simulated, and the models are compared with their fixed parameter counterparts. We show that the FVECM–GAS models perform better in the cases shown here, and thus extend the FVECM model in a useful way. We also note that an approach with fixed parameters may lead to negligence of the cointegration relationship, providing another source of errors.