In contrast, if a wave record could be represented by any 
number of discrete spectral components with, say, four place ac- 
curacy for the spectral periods, then it is theoretically possible 
to predict the wave records into the future for a long time. For 
example, suppose that a wave record were actually composed of three 
Sine waves of amplitudes A,, A>, and Aas with periods of 8.75, 
10.35, and 14.10 seconds, respectively, and that the numbers actually 
mean that the periods are between 8.745 and 8.755, 10.345 and 10.355, 
and 14.095 and 14.105. Then after one thousand seconds (17 minutes), 
the greatest possible predicted phase error would be 24 degrees. 
At a point in the future one thousand seconds ahead at which, say, 
theoretical positive cosinusoidal reinforcement is to occur the 
predicted amplitude would have to be between Ay + Ay + A, and 
A, cos 2325° + A,cos 16.8° + A,cos 9°, The autocorrelation function 
implies that such accuracy is fallacious, that a wave record cannot 
be predicted that far into the future for "sea" conditions, and that 
the sea surface cannot possibly be composed of discrete spectral 
components. 
Wiener [1949] has given the mathematical procedure for predict- 
ing the future behavior of a stationary time series given its past. 
From the past, the first step is to find an estimate of the auto- 
correlation function. The autocorrelation function can then be 
used to determine the kernal of an integral equation such that when 
the past of the record is multiplied by the kernal and integrated 
over past time, a number results which is the best possible forecast 
for the value which will occur, say, thirty seconds into the future. 
The best possible forecast is in the least square sense; that is, 
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