A Seasonal Autoregresslve Model of the 

 Anchovy Engraulis encrasicolus Fishery 

 In the Eastern Mediterranean 



Konstantinos I. Stergiou 



National Centre for Marine Research 



Agios Kosmas, Hellenikon, Athens 16604. Greece 



Accurate forecasting is a difficult 

 issue mainly because forecasters are 

 confronted by all sorts of uncertain- 

 ty (in resource production, budgets, 

 political decisions, etc.) (Hilbom 1987). 

 Although not widely employed, Auto- 

 Regressive Integrated Moving Aver- 

 age (ARIMA) stochastic models 

 (Box and Jenkins 1976) have been 

 successful in describing and fore- 



casting the fishery dynamics of a 

 wide variety of species (lobster: 

 Boudreault et al. 1977, Saila et al. 

 1979; tuna: Mendelssohn 1981; pil- 

 chard: Stergiou 1989a). Although 

 multivariate, deterministic models 

 (e.g., regression models: Ryan 1986, 

 Koslow et al. 1987) are more com- 

 mon in fishery forecasting, these 

 deterministic models often suffer 



Figure I 



Monthly catches of 

 anchovy in Greek 

 waters, January 

 1964-December 

 1986. 



I 2ee6 



rv^V^ 



2 4 S 



MONTH <1=JAN, . 



le 12 



Figure 2 



Seasonal subseries 

 plot of monthly 

 catches of anchovy 

 in Greek waters, 

 1964-86. Horizontal 

 lines represent the 

 average catch of 

 each month. Vertical 

 lines are plotted 

 from the average 

 catch to the actual 

 catch of each year of 

 the 1964-86 period. 



from (1) artificial correlations intro- 

 duced to the data, (2) residual auto- 

 correlation, (3) high residual vari- 

 ance, and (4) colinearity between the 

 independent variables that may bias 

 the fit (Stergiou 1989b, In press). 



In this note, a seasonal autoregres- 

 slve model is presented that pro- 

 duces forecasts of the monthly purse- 

 seine catches of anchovy Engraulis 

 encrasicolus in Greek waters. The 

 anchovy is one of the most impor- 

 tant pelagic fish, in terms of bio- 

 mass, in the Mediteranean Sea. Mean 

 annual anchovy catch in Greek waters 

 during 1982-85 amounted to 12 820 

 t, representing 17% of the total 

 marine catch (Stergiou 1989b). Of 

 the anchovy catch in Greek waters, 

 96% is attributed to the purse-seine 

 fishery, accounting for 26% of the 

 total purse-seine catch (Stergiou 

 1986a, b). Monthly catches of an- 

 chovy for January 1964-December 

 1986 (Fig. 1) (National Statistical 

 Service of Greece 1968-88) show a 

 marked seasonal pattern (Figs. 1, 2) 

 and an increasing trend in the vari- 

 ability of monthly catches for the 

 years following 1980. The latter 

 may indicate that anchovy has suf- 

 fered recruitment overfishing in re- 

 cent years (since the late 1970s, 

 purse-seine fishing in Greek waters 

 is anchovy-oriented rather than pil- 

 chard-oriented due to the higher 

 price of anchovy [Stergiou 1986b, 

 1989a, 1990]). 



The ARIMA processes (Box and 

 Jenkins 1976, Makridakis et al. 1983) 

 apply to stationary series (time 

 series with no systematic change in 

 mean and variance and free of peri- 

 odic variations). First- or second- 

 order differencing (nonseasonal 

 and/or seasonal) handles problems 

 of nonstationarity in the mean, and 

 logarithmic (or power) transforma- 

 tion of the raw data handles nonsta- 

 tionary variance. The general form 

 of the ARIMA models, 



Manuscript accepted 28 December 1989. 

 Fishery Bulletin, U.S. 88:411-414. 



411 



