Appendix

For the estimation of parameters, the linear first-order error correction model

was reformulated as an ARMA(1, 1) process based on a Gaussian white noise series wj, ..., wN with variance oW.

The asymptotic autocovariance function of the process described in Equation (19.4) can be derived as (Vorberg and Schulze, 2002; Vorberg and Wing, 1996)

and the asymptotic autocovariance function for the ARMA(1, 1) model, described in Equation (19.5) (Shumway and Stoffer, 2000):

From this we can extract the three equivalences

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