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Young, P.C., Pedregal, D.J. and Tych, W. (1999) Dynamic harmonic
regression. In press, Journal of Forecasting.
This paper describes in detail a flexible approach to nonstationary time
series analysis based on a Dynamic Harmonic Regression (DHR) model of the
Unobserved Components (UC) type, formulated with a stochastic state space
setting. The model is particularly useful for adaptive seasonal adjustment,
signal extraction and interpolation over gaps, as well as forecasting or
backcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are
exploited for estimating the various components, with the Noise Variance
Ratio and other hyper-parameters in the stochastic state space model
estimated by a novel optimisation method in the frequency domain. Unlike
other approaches of this general type, which normally exploit Maximum
Likelihood methods, this optimisation procedure is based on a cost function
defined in terms of the difference between the logarithmic pseudo-spectrum
of the DHR model and the logarithmic autoregressive spectrum of the time
series. This cost function not only seems to yield improved convergence
characteristics when compared with the alternative ML cost function, but it
also has much reduced numerical requirements.
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