Refined instrumental variable methods of recursive time-series analysis Part I. Single input, single output systems

This paper is the first in a series concerned with a comprehensive evaluation of the refined instrumental variable-approximate maximum likelihood (IVAML) method of time-series analysis. The implementation of a recursive/iterative version of the refined IVAML algorithm for single input, single output systems is discussed in detail and the performance of the algorithm is evaluated by Monte-Carlo simulation analysis applied to five simulated stochastic systems. As conjectured, the algorithm appears to yield asymptotically efficient estimates of the time-series model parameters and, indeed, it seems to approach minimum variance estimation of the basic system model parameters for even low sample size and low signal/noise ratios. The noise model parameters are not estimated so well at the smaller sample sizes but the estimation performance appears similar to that of other competing methods of analysis, such as recursive maximum likelihood (RML). Subsequent papers on this same general topic will deal with extensions of the refined IVAML procedure to handle multivariate systems, time-variable parameters and the estimation of continuous-time systems described by ordinary differential equations.