USING BOX-JENKINS MODELS TO FORECAST FISHERY 

 DYNAMICS: IDENTIFICATION, ESTIMATION, AND CHECKING 



Roy Mendelssohn' 



ABSTRACT 



Box-Jenkins models are suggested as appropriate models for forecasting fishery dynamics. Unlike 

 standard production models, these models are empirical, dynamic, stochastic models. Box-Jenkins 

 models are not biased when estimating relationships between catch and effort, as are standard 

 production models. The use of these techniques is illustrated on catch and effort data for the skipjack 

 tuna fleet in Hawaii. An actual 12-month forecast is shown to give a reasonable fit to the observed data. 

 Most of the discrepancies are explained by changes in the behavior of the fishermen (i.e., economic 

 factors), rather than by lack of knowledge of the behavior of fish. 



Accurate forecasting models would be useful in 

 fishery management because extended jurisdic- 

 tion and international agreements require pre- 

 seasonal predictions of the actual catch of a fleet. 

 In addition, improved forecasts of fish availability 

 can lead to improved planning by fishermen or by 

 processing firms. Forecasting techniques have 

 expanded greatly in the last years, but few have 

 been adapted to research in fisheries manage- 

 ment. Instead, techniques designed to establish 

 the equilibrium health of the stocks are also being 

 used to attempt dynamic forecasting. 



At present, two least squares procedures are 

 being used to estimate the general production 

 model, the search procedure of Pella and Tom- 

 linson (1969) and the weighted least squares of 

 Fox (1970, 1971, 1975). The Fox procedure fits 

 catch per unit effort against a function of lagged 

 effort. Several authors (Chayes 1949; Eberhardt 

 1970; Atchley et al. 1976) have demonstrated that 

 scaling the dependent variable (i.e., catch) by 

 the independent variables (i.e., effort) biases 

 the fit by introducing artificial correlation into 

 the data. Johnston (1972) showed that ordinary 

 least squares gave biased estimates and an in- 

 flated F- statistic when used with variables lagged 

 on themselves. Neither the Fox nor the Pella- 

 Tomlinson procedure accounts for the effect of 

 autocorrelated errors in the estimation procedure 

 which Granger and Newbold (1977) and Newbold 

 and Davies (1978) have demonstrated bias both 

 estimation and tests of fit. An examination of the 



residuals in Fox (1971, figure 3B) clearly shows 

 them to be autocorrelated. Residuals from many 

 spawner-recruit curves display similar behavior. 



In this paper, the use of Box-Jenkins models 

 for modeling and forecasting fisheries dynamics 

 is explored. Box-Jenkins and other related fore- 

 casting techniques are specifically designed for 

 estimating and testing models in the presence 

 of autocorrelated errors. The fitted models are 

 stochastic rather than deterministic, thus reflect- 

 ing the variability found in most fisheries. The 

 models are constructed empirically, and are best 

 suited for forecasting. The models tell us little 

 about the long-term health of the stocks, so that a 

 judicious use of production, yield per recruit, and 

 accurate forecasting models is required to give the 

 best overall picture of the fishery. 



My preference for Box-Jenkins models over 

 other forecasting methods now available is due to 

 the good documentation (see for example Ander- 

 son 1975; Box and Jenkins 1976; Granger and 

 Newbold 1977) and computer accessibility The 

 results presented here were obtained using a 

 package originally developed by David Pack at 

 Ohio State University and now available through 

 Automatic Forecasting Systems.^ 



The three-step process of model identification, 

 model estimation, and model diagnostic checking 

 is illustrated by developing a model that makes 

 monthly forecasts of skipjack tuna, Katsuwonus 

 pelamis, catches in Hawaii. Experience with the 

 model suggests that for a 12-mo forecast of catch. 



'Southwest Fisheries Center Honolulu Laboratory, National 

 Marine Fisheries Service, NOAA, Honolulu, HI 96812. 



Manuscript accepted May 1980. 



FISHERY BULLETIN; VOL. 78, NO. 4, 198L 



^Reference to trade names does not imply endorsement by the 

 National Marine Fisheries Service, NOAA. 



887' 



