Sunspots: Power Spectra and a Forecast.
AIR FORCE GEOPHYSICS LAB HANSCOM AFB MA
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High resolution power spectra of the Zurich sunspot numbers for the period 1849 to 1978 are obtained using the maximum entropy technique of Burg. The monthly means are first smoothed using a digital, least-squares, band-pass filter with 193 weights, and then decimated to obtain a more manageable series. An overall power spectrum, which displays multiple structure and harmonic series is then obtained. In order to explain the complications in the spectrum, a dynamic spectrum is displayed. This is obtained by finding the spectra of data samples 66 years long, repeatedly slipped by 2 years for a total of 78 spectra. The spectra are then much simpler and vary smoothly with epoch. The nominal 11-year line varies in period from about 10 to 12 12 years. In the process of obtaining a power spectrum a prediction error filter is derived. This linear filter may then be used to make predictions as follows using sets of data containing 5 solar cycles of unsmoothed monthly values beginning with cycles 9 through 15, predictions of the next 12 months of the time series are made and compared to the observed values. RMS errors vary between 5 and 33 and lead to an expectation that the error of prediction for cycle 21 will be about 20. The entire cycle 21 is then predicted using 50, 100, 150 prediction error coefficients. The maximum of cycle 21 is predicted to be 130 or - 20 at 1980 .1 or - 0.2. Author