Recent developments in the signal processing field of electrical engineering have resulted in several frequency domain methods of extrapolating a time series. Insight gained in testing one such method, the Papoulis algorithm, has been used to suggest modifications which greatly improve its performance under most operating conditions where real data are concerned.
The modified Papoulis method thus developed has been applied to electricity load forecasting over the short and medium term, as well as to world economic and energy data, to assess the cyclic structure present in each series about a trend.
KEY WORDS Spectral estimation Time series analysis Forecasting
Extrapolation Super-resolution Time series analysis and forecasting are commonplace in fields ranging from physics to politics. Perhaps the largest, and arguably the most important, use for time series analysis is in the production of mathematical models which describe economic and industrial time series. The form of these models usually fits into one of two categories: time domain models, such as the autoregressive and moving average, or frequency domain models in the form of a frequency spectrum. Each of these forms is widely used for analysis, but in obtaining forecasts only the time domain approach is used. This is a result of the difficulties encountered when computing spectra for finite duration real data time series.
Recent advances in the signal processing field of engineering have provided solutions to some of these problems. Furthermore, a few of the super-resolution and signal extrapolation algorithms developed use the fast Fourier transform (Cooley and Tukey, 1965) to perform the bulk of the calculations. The resultant simplicity of application and interpretation combined with inherent computation speed make such algorithms highly attractive.
In this paper a fast Fourier transform based super-resolution algorithm is adapted for use in spectral estimation and forecasting. It is constructed around an algorithm devised by Papoulis (1975) and represents a significant improvement over any of the spectral identification or signal