The investigation of the square of the multiple correlation coefficient 

 suggested that about 10 years of record are sufficient for certain curve-fitting 

 and estimation problems. It has just been concluded that there is no such break 

 in the variability of the autocorrelation coefficient as a function of record length. 

 Thus a decision as to the sample length necessary to obtain useful estimates of 

 the autocorrelation function must be made on some absolute basis, or a cost func- 

 tion must be introduced such that a combination of increasing cost and decreasing 

 variability with sample size results in an optimization problem. 



Two additional comments are pertinent. First, figure 4 shows the auto- 

 correlation functions for samples of 8, 10, and 20 years, respectively. Attention 

 is called to the 10-year records. It appears that the autocorrelation functions 

 agree well out to a lag of about 80 days. Second, autocorrelation functions for 

 the same record lengths have been averaged by lags, and are shown in figure 5. 

 There is a strong indication that autocorrelation functions from finite samples 

 are biassed. Restricting the discussion to lags out to 80 days, and assuming 

 the autocorrelation function for the 40-year sample is close to the true function, 

 the mean functions for 5- and 8-year samples are badly biassed with little bias 

 indicated in the 10- and 20-year mean functions. It is concluded that 10-year 

 samples provide consistent and usable autocorrelation functions out to a lag of 

 80 days. 



16 



