Dynamic harmonic regression

This paper describes in detail a flexible approach to nonstationary time se ries analysis based on a Dynamic Harmonic Regression (DHR) model of the Uno bserved Components (UC) type, formulated within a stochastic state space se tting. The model is particularly useful for adaptive seasonal adjustment, s ignal extraction and interpolation over gaps, as well as forecasting or bac kcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are exp loited for estimating the various components, with the Noise Variance Ratio and other hyperparameters in the stochastic state space model estimated by a novel optimization method in the frequency domain. Unlike other approach es of this general type, which normally exploit Maximum Likelihood methods, this optimization procedure is based on a cost function defined in terms o f the difference between the logarithmic pseudo-spectrum of the DHR model a nd the logarithmic autoregressive spectrum of the time series. The cost fun ction not only seems to yield improved convergence characteristics when com pared with the alternative ML cost function, but it also has much reduced n umerical requirements. Copyright (C) 1999 John Wiley & Sons, Ltd.