Signal Coherence and Spectrum M. J. Hinich Dates Sunspot Numbers First datum used 1 Last datum used 58270 Sample size = 58270 ============================================================ Segment Length = 58270 Number of Segments = 1 Sampling interval = 1.00000 day Resolution Bandwidth = 3966. day No. Frames = 14 Frame Length = 3966 Passband ( 3966.00 20.03 ) day No. of frequencies in band 198 Spectrum is not smoothed Coherence threshold for the coherent part of the frame = 0.3000 Probability tail value threshold for the AR fit iterations = 0.0100 ============ Column 1 ============ ************************************************************ Descriptive Statistics of Data Used = 58270 ============================================================ Mean = 55.8 Std Dev = 52.3 Skew = 1.21 Kurtosis = 1.40 C(6) = -5.874 Max value = 355. Min value = 0.00 ************************************************************ Descriptive Statistics of AR Residuals ============================================================ Mean = -0.297E-02 Std Dev = 13.3 Skew = 0.337 Kurtosis = 3.73 C(6) = 53.429 Max value = 114. Min value = -97.6 Whiteness test statistic p-value = 0.000 ************************************************************ AR( 8) parameters / t values Adjusted R Square = 0.935 Std Error of AR Fit = 13.3 p Value Threshold for the Iterative AR Prewhitening Method = 0.010 =============================================== 1 - 0.97 2 - 0.06 3 - -0.04 5 - -0.04 6 - -0.03 8 - 0.05 234.23 9.84 -8.09 -7.77 -5.42 17.28 Amplitudes & Periods of the Roots of the AR Polynomial in units of day A real root is given a period = 0. =============================================== 1 - 0.73 2 - 0.73 3 - 0.97 4 - 0.97 5 - 0.97 6 - 0.97 7 - 0.97 8 - 0.97 13.43 13.43 0.00 0.00 0.00 0.00 0.00 0.00 ************************************************************ Descriptive Statistics of the Modulation ============================================================ Mean = 0.707E-08 Std Dev = 12.7 Skew = 0.185 Kurtosis = 3.66 C(6) = 48.766 Max value = 104. Min value = -92.5 ============================================================ 1 -period= 3966.00000 2 -period= 1983.00000 3 -period= 566.57141 4 -period= 264.39999 5 -period= 180.27272 6 -period= 172.43478 7 -period= 132.20000 8 -period= 116.64706 9 -period= 113.31429 10-period= 110.16666 11-period= 104.36842 12-period= 94.42857 13-period= 92.23256 14-period= 90.13636 15-period= 84.38298 16-period= 73.44444 17-period= 70.82143 18-period= 69.57895 19-period= 66.10000 20-period= 52.18421 21-period= 47.21429 22-period= 44.06667 23-period= 43.10870 24-period= 41.74737 25-period= 41.31250 26-period= 40.88660 27-period= 36.72222 28-period= 35.72973 29-period= 34.48696 30-period= 34.18966 31-period= 33.61017 32-period= 33.05000 33-period= 32.77686 34-period= 32.50820 35-period= 32.24390 36-period= 31.22835 37-period= 30.98438 38-period= 30.50769 39-period= 29.37778 40-period= 29.16176 41-period= 28.94891 42-period= 28.53237 43-period= 28.32857 44-period= 25.10126 45-period= 24.18293 46-period= 22.15643 47-period= 22.03333 48-period= 21.67213 49-period= 21.55435 50-period= 21.09575 51-period= 20.65625 52-period= 20.23469 53-period= 20.13198 54-period= 20.03030 Segment 1 p-value = 0.00020 ============================================================ Header for Output in *.graph file Period day , Log Spectrum (dB), Coherence, Chi-Square Probability, Periodogram Format: (19x,f3.0) Large Sample Standard Error = 1.161 Number of Data Columns = 1 Version 1-12-2009 Date & Time Mon Jan 12 11:07:19 2009 Elapsed time = 0.30 secs