94 



Fishery Bulletin 105(1) 



A Winter skate 



G Yellowtail flounde 



1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i^i 1 1 1 1 1 1 1 1 1 1 1 1 1 



1965 1970 1975 1980 1985 1990 1995 2000 



B Little skate 



E Atlantic cod 



 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i Jl I 1 1 1 1 1 1 



1965 1970 1975 1980 1985 1990 1995 2000 



-»- Original 

 ^ Smoothed 



Year 



C Atlantic herring 



B 1 1 1 aAI 1 1 1 1 h 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 



F Haddock 



I Atlantic mackerel 



'm- * 



Iti 1 1 J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ijji 1 1 1 I I I 1 1 1 1 



1965 1970 1975 1980 1985 1990 1995 2000 



Figure 2 



Comparison of original time series of estimated total biomass on Georges Bank from the spring bottom trawl survey (filled 

 circles) and inverse-transformed, ARIMA-smoothed time series (open triangles) for nine finfish species. 



Atlantic herring (fall, Fig. 3C), haddock (spring, Fig. 

 2F), yellowtail flounder (spring. Fig. 2G; fall, Fig. 3G), 

 winter flounder (Pseiidopleiironectes ainericanus) (fall, 

 Fig. 3H), and Atlantic mackerel (spring, Fig. 21). A 

 high degree of smoothing occurred for Atlantic herring 

 (spring. Fig. 2C), silver hake (fall. Fig. 3D), Atlantic 

 cod (Gadus morhua) (spring. Fig. 2E; fall. Fig. 3E), 

 winter flounder (spring, Fig. 2H), and Atlantic mack- 

 erel (fall, Fig. 31). 



Impressions obtained from visually comparing the 

 original and smoothed time series were consistent with 

 the fraction of innovation variance (K loj. Tables 2 and 

 3) in the observed time series ascribed to observation 

 error. Recall that we chose to perform the maximal 

 amount of smoothing possible (i.e., taking a^f=K in Eq. 

 13). Our visual classifications fell fairly neatly into the 

 following categories based on K la]-: 1) a low degree of 

 smoothing corresponded to /iL'*/a/<0.25, 2) a moderate 

 degree of smoothing corresponded to 0.25< /r/q/<0.60. 



and 3) a high degree of smoothing corresponded to 

 0.60s/r/a/. 



In addition, it appeared that the degree of smoothing 

 varied inversely with the order of the moving average 

 component of the ARIMA model for the observed time 

 series. When the order of the moving average component 

 was greater than 2, the degree of overall smoothing was 

 typically small. Substantially more smoothing was evi- 

 dent when the order of the moving average component 

 was 1, because of the equivalence with an exponentially 

 weighted smoother. 



The nine time series found to be RWPUN processes 

 provided a means to check whether our choice to per- 

 form the maximal amount of smoothing was reasonable. 

 For such time series, the value of the moving average 

 coefficient, i),, is equal to the ratio of the observation 

 noise variance, a'^, to the innovation variance a'] . Con- 

 sequently, oJrij = o/. For eight of the nine series, the 

 ratio of a.^ to K' was greater than 80% (Table 4). 



