in the resulting coefficients will measure the effect of 

 missing data. The generation of many such time series to 

 give estimates and confidence limits for parameters is an 

 example of the technique which has been given the name 

 Monte Carlo. 



The major interest in the jS's as statistical variables 

 is the variability from sample to sample of their deviations 

 from some true, but unknown, values. For an integral 

 number of years of complete time series, the four estimates 

 of the variances of j8 1 , fi , fl , and /S , as obtained from 

 the inverse matrix, are equal. Figures 5A, 5B, 6A, and 

 6B are histograms of the differences between the /3's of 

 120 independently generated sample time series and the 

 corresponding jS's of the complete time series for 7 years 

 of Scripps Pier and Triple Island data. The jS's are uncor- 

 rected and have equal variances. Because of the effective 

 increase in sample size, the differences have been grouped 

 for the four jS's. For figures 5 A and 6 A the sample time 

 series average 50 percent missing data; for figures 5B and 

 6B they average 20 percent missing data. The histograms 

 are presented to demonstrate that the differences are sym- 

 metrically distributed about zero, and to show the dispersion. 



Figure 7 is a plot of jS vs /3 X for a sample time series. 

 It is included to demonstrate that the jS's are uncorrelated. 

 Table 2 presents the correlation coefficients B for all com- 

 binations of jS's for the 7-year sample time series with 50 

 percent of the data missing. The 5 percent critical value of 

 B is 0. 179. One of the twelve 7?'s barely exceeds this value. 

 This not unlikely event has prior probability 0. 34. 



20 



