MENDELSSOHN: USING BOX-JENKINS MODELS IN FISHERY DYNAMICS 



Table 5. — Estimated autocorrelation function for residuals of effort model for the Hawaii skipjack tuna 



fleet, 1964-78. 



Table 6. — Estimated autocorrelation function for residuals of catch model for the Hawaii skipjack tuna 



fleet, 1964-78. 



Table 7. — Parameter estimates for effort model. Model (2) 

 (see text). (Based on 180 observations.) 



backforecasting is used in estimating the pa- 

 rameters for Models (4) and (5). The chi-square 

 statistics show no reason to suspect model inade- 

 quacy. The residuals show no significant cross- 

 correlation with total catch, when l/V 180 (180 

 observations in the series) is used as a rough 

 standard error. The residual autocorrelation func- 

 tion shows spikes around lag 15 that are higher 

 than would be desired, but overall the fit is 

 reasonable, and the model residuals could reason- 

 ably be modeled as white noise. 



DISCUSSION AND FORECASTS 



Two transfer function models and one univari- 

 ate model have been used to forecast the catch and 

 effort in the skipjack tuna fishery during 1979. It 

 is worth emphasizing that the original 12-mo fore- 

 casts were made in January 1979 and the updated 

 forecasts were made in May 1979, so the reported 

 results are true forecasts — there was no a priori 

 knowledge of the data to help improve the "fit" of 

 the forecasts. The original catch and effort fore- 

 casts are given in Tables 12 and 13 while the 

 updated catch forecasts are given in Table 14. 



The models used to produce the forecasts are 

 best understood when written out in difference 

 equation form. The univariate model for catch is: 



yt = yt-s.2 + iat + 0.538a/-i + 0.438a;-2 + 0.412a^-3 + 0.309a;-4) (6) 

 - (0.996ai-i2 + 0.5350^-13 + 0.436a;-i4 + 0.410a<-i5 + O.SOSa^-ie), 



893 



