Refined instrumental variable methods of recursive time-series analysis Part II. Multivariable systems

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Abstract
This paper describes the refined IVAML algorithm for estimating the parameters in the multivariable analogue of the single input,. single output model considered in Part I. It also shows that similar refined algorithms can be constructed for other multivariable model forms, including the ARMAX, dynamic adjustment (DA) with autoregressive errors and the multivariable transfer function (MTF). The performance of the algorithm is evaluated by Monte Carlo analysis applied to four simulation models with between 25 and 39 parameters and it is carried out for various sample sizes and signal/noise ratios. As in the SISO model version, the analysis indicates that the algorithm yields asymptotically efficient estimation results, whilst providing low variance estimates of the basic system parameters for medium sample sizes.