MODEL FOR MISSING DATA 



It is proposed that the effect of missing data be 

 evaluated in the following manner. There exist series of 

 sea surface temperatures for which there are no missing 

 data (Scripps Pier), or almost none (Triple Island), over 

 periods of several years. Complete series of length up to 

 12 years can be selected from each of these sources. The 

 few missing temperatures for Triple Island are filled in by 

 adding to interpolated values random normal deviates having 

 the appropriate variance. The complete series remains 

 unchanged thereafter. It is thought necessary to consider 

 two stations, whose time series of sea-surface temperatures 

 have slightly different characteristics with respect to 

 residual variability and significance of semiannual oscilla- 

 tory terms, in order to avoid decisions which might be too 

 dependent on the characteristics of a single station. 



Regression and autocorrelation analyses are performed 

 on the complete series. Estimates of the variances of the 

 regression coefficients /3 are available from the matrix in- 

 verse to that of the coefficients in the normal equations of 

 the least squares analysis. The estimates of the variances 

 used assume independent, equal variance residuals. These 

 variances are attributable to the residual variability of 

 observations about the true regression curve. 



The 40 years of Scripps Pier residuals with very few 

 missing observations provide an estimate of the variance 

 of the near-zero autocorrelation coefficients. The autocor- 

 relation function for Scripps Pier was computed out to a lag 

 of 1800 days, an arbitrary figure slightly over 10 percent 

 of the total sample length. The standard deviation of the 

 autocorrelation coefficients with lags from 400 days (end of 

 the initial decay of the function) to 1800 days is a = 0. 293. 

 This estimate of o" c is considered to be the best available 

 measure of the random variability of the near-zero auto- 

 correlation coefficients of sea-surface temperature anomalies. 

 It is based on a large sample of the autocorrelation coefficient, 

 and the maximum lag involved is still only a small fraction 

 of the total time series length. 



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