MENDELSSOHN: USING BOX-JENKINS MODELS IN FISHERY DYNAMICS 



representation of Model (1). The value of Bi is 

 nearly one. Thus the term (1 - B^^) appears on 

 both sides of the equation, and can be cancelled. 

 Abraham and Box (1978) showed that this is 

 sufficient reason to suspect a deterministic cosine 

 function trend with a moving average model 

 around the trend. Given the high residual mean 

 square for the model (115, 170), this latter inter- 

 pretation is consistent with the folklore on the 

 fishery — highly variable but on the average 

 things are similar from year to year. 

 The first transfer function model is: 



within 89c of the observed total catch, and for the 

 period July 1977- December 1978 the model fore- 

 casted within 12% of the observed total catch. 



Except for June 1979, the summer months were 

 predicted accurately. Experience with the model 

 on the data from July 1977 suggests that the 

 summer months are almost always predicted 

 within 10% of the observed catch. In fact, in March 

 1979, an industry representative doubted the high 

 catch forecasted for the summer, due to the low 

 catch in January and February 1979. Similarly, 

 the sharp drop in catch in September was pre- 



yt = 8.003X? + (yt-i2 - 8.003xr-i2) + (at + 0.489a^-i + 0.326a;-2 + 0.149a(-3 + 0.175a<- 

 - (0.996a?-i2 + 0.487a;-i3 + 0.325ai-i4 + 0.148a^-i5 + 0.174a/-i6). 



) (7) 



This model has an interpretation similar to that 

 of the univariate model, except now catch per 

 weighted units of effort are compared between 

 years. The second transfer function model com- 

 pares lagged values of catch and effort also. 



It is difficult to judge the value of a forecast, 

 since this will depend on the use being made of the 

 forecast and the alternatives available. Granger 

 and Newbold (1977) suggested the most appropri- 

 ate measure of the value of a forecast is a loss 

 function which reflects the loss from inaccurate 

 forecast in the actual application for which the 

 forecasts were developed. For forecasting the skip- 

 jack tuna fishery in Hawaii, there were four 

 immediate goals. The first was to give a reason- 

 ably accurate estimate of total catch over the 

 year, within a 15-20% error rate. The second 

 was to predict what kind of summer it would be. 

 May through September being the main fishing 

 months. This means predicting what month the 

 fish start running, what month the fish stop 

 running, and whether the catch is high and 

 peaked as in 1979, or flat and low as in 1978. An 

 important concern is the relative size of the drop 

 in catch when it occurs in September or October. 



A third concern was an accurate forecast of the 

 catch in December, when the holiday demand for 

 Sashimi (a Japanese raw flsh delicacy) drives 

 prices very high. And finally, an increased under- 

 standing of the dynamics of the fishery was 

 desired. 



Based on these criteria, I feel the forecasts have 

 performed well, especially compared with any 

 alternative available. The error in predicting the 

 1979 total catch is higher than desired. However, 

 for the last 6 mo of 1977 the model forecasted 



dieted by the model. Again, in August 1979 an 

 industry representative doubted that a sharp 

 decline in catch would occur in September, but 

 said that this could be a useful piece of knowledge 

 since their decisions would change if they knew 

 they could expect the supply to drop sharply. 



The forecasts have provided insight into the 

 fishery. The major failures of the forecasts were 

 January 1979 and October-December 1979. Jan- 

 uary 1979 was a period of unusually bad storms, so 

 that few fishing trips were made. However, the 

 observed catch per trip was 0.993 metric tons (t), 

 while Model (4) predicted a catch per trip of 1.033 1. 

 The main source of the error in the forecast was 

 the predicted number of trips to be made. 



Similarly, the high summer catches, coupled 

 with very high catches of yellowfin tuna, drove the 

 price for skipjack tuna to very low levels. At the 

 end of September, most of the boats went into 

 drydock because of the prevailing low prices. The 

 few boats that remained tended not to be the 

 industry leaders (i.e., boats with a proven record of 

 higher catch rates), and made only short forays 

 rather than their usual fishing trips. 



The point of these explanations is that the 

 causes of the poor forecasts appear to be related 

 not to the behavior of the fish stocks but rather to 

 the behavior of the fishermen. Therefore, the 

 effort to improve the forecasts needs to be di- 

 rected at understanding the fishery, rather than 

 the fish. (An economic study of the industry is 

 near completion.) 



Finally, water temperature and salinity data 

 for one location off Oahu were included in the 

 transfer function models. These variables added 

 little to the forecasts, and since there is no 



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