CPUE did not change over time (i.e., no power plant effect). A "change" 



could be an increase or decrease in the average values (trend) , or an 



alteration of the frequency or amplitude of the fluctuations (cyclical 



components) of the values over time. While these specific changes can 



be tested with time series methodology (Box and Jenkins 1976), as a 



first step an alternate approach was taken. The monitoring data collected 



prior to the current year were used to construct autoregressive time 



series models of CPUE. Because long term constant values were hypothesized, 



the data were not detrended (long term trend removed from the data by 



regression) . Detrending data that are primarily the results of stochastic 



processes is a procedure that may give misleading results in forecasting 



models (Box and Jenkins 1976) . Autocorrelations between the catch at 



time, i, and 'n' time units, away, (up to 26 in this case) were determined. 



If such correlations were significantly different from zero at ct = 0.05, 



autoregressive terms of "A " were included in the model. For example, 



if the total catch was found to be positively correlated with its value 



12 months away, the time series model for forecasting total catch would 



include an autoregressive term for 6 lags (bimonthly data points) , 



designated A,. Constants and autoregressive terms were determined. 



These models were used to forecast the catch for the current year. The 



forecasted data were compared to the actual catch by using a test 



statistic with an F distribution: 



s 

 £ (a ± - f ± ) 2 /(s-1) 



F calc = i=1 (12) 



where a.^ = actual data point for time period i 



f^ = forecasted date point for thime period i 

 s = number of time periods forecasted 

 o = least square estimate of the model variance 



45 



