This reformulation has two important advantages. First, the estimation of parameters of the linear first-order error correction model can be accomplished using the standard methods for ARMA(1, 1) models. In practice, this was accomplished by using the ARMAX routine in MATLABTM (System Identification Toolbox), which uses the iterative Newton-Raphson method to minimize the quadratic next-step prediction error. The second advantage is that the characteristics of the model only vary with ^ and 9, but are homogenous across different levels of the parameter aW. For example, whereas optimal error correction aOPT is a nonlinear function of a2M and a2T (Vorberg and Wing, 1996), it is a linear function of 9 and independent of aW.

The region of parameter space encompassing and near the region of optimal error correction is of importance in the estimation process since the model becomes unidentifiable here. The time series under this model becomes Gaussian white noise with autocovariance function la2; k = 0 Y(k) = \ w (19.14)

Monte Carlo studies of this method have shown that the parameter values for a, aM, and can be validly estimated from simulated time series data produced following Equation (19.4). However, in the region surrounding the line of indeterminacy (Equation (19.13)), the estimates become unreliable (Schulze^ and Vorberg, 2002). In practice, we avoid this region by excluding trials in which y( k) does not significantly deviate from zero for the lags 0 < k < 6.

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