Multiple input transfer function noise modelling in the time and frequency domain: empirical evidence from Monte Carlo simulations

In the present study we have evaluated two competing methods for estimation of the impulse response weights used in the identification of transfer function models: a time domain method involving biased regression techniques and a frequency domain method utilizing a discrete Fourier transform of the cross-covariance system of the transfer function model. The algorithms were implemented on a VAX-8800 computer at the Computing Center at Abo Akademi. The evaluation of the competing methods was carried out by simulations of different transfer function noise model structures. The models are essentially the same as those of Edlund, but we have used a far greater number of replications in the cases tested. Furthermore, we have used actually identified and estimated autoregressive integrated moving-average models of the residuals in the identification procedure of impulse response weights, in contrast with Edlund who only used theoretical noise models in filtering the input and output series. After a short discussion of the underlying theory, we present the procedures and results of the empirical testing.