Abstract— Abundance indices derived 

 from fishery-independent surveys 

 typically exhibit much higher inter- 

 annual variability than is consistent 

 with the within-survey variance or 

 the life history of a species. This extra 

 variability is essentially observation 

 noise (i.e. measurement error); it prob- 

 ably reflects environmentally driven 

 factors that affect catchability over 

 time. Unfortunately, high observa- 

 tion noise reduces the ability to detect 

 important changes in the underlying 

 population abundance. In our study, a 

 noise-reduction technique for uncor- 

 related observation noise that is based 

 on autoregressive integrated moving 

 average (ARIMA) time series mod- 

 eling is investigated. The approach 

 is applied to 18 time series of fin- 

 fish abundance, which were derived 

 from trawl survey data from the U.S. 

 northeast continental shelf. Although 

 the a priori assumption of a random- 

 walk-plus-uncorrelated-noise model 

 generally yielded a smoothed result 

 that is pleasing to the eye, we rec- 

 ommend that the most appropriate 

 ARIMA model be identified for the 

 observed time series if the smoothed 

 time series will be used for further 

 analysis of the population dynamics 

 of a species. 



Removing observational noise from 

 fisheries-independent time series data 

 using ARIMA models 



William T. Stockhausen (contact author) 

 Michael J. Fogarty 



Email address for W. T, Stockhausen; William. Stockhausenta'noaa.gov 



National Ocean and Atmospheric Administration 



National Marine Fisheries Service 



Northeast Fisheries Science Center 



166 Water Street 



Woods Hole, MA 02543 



Present address for corresponding author; National Marine Fisheries Service 



Alaska Fisheries Science Center 

 7600 Sand Point Way NE 

 Seattle, Washington 98115 



Manuscript submitted 12 November 

 2004 to the Scientific Editor's Office. 



Manuscript approved for publication 

 18 April 2006 by the Scientific Editor. 



Fish. Bull. 107:88-101 (2007). 



Time series of species abundance from 

 fishery-independent surveys, such as 

 bottom trawl or acoustic surveys, are 

 important in monitoring temporal 

 change in the abundance of marine 

 populations. For commercially impor- 

 tant species, catch and effort data 

 from the commercial fishery may be 

 available, allowing estimation of tem- 

 poral trends of the stock population 

 by means of stock assessment models 

 (e.g., virtual population analysis). 

 However, such records are not avail- 

 able for many species, especially those 

 with little commercial (but perhaps 

 significant ecological) value. Fishery- 

 independent surveys may thus con- 

 stitute the only source of information 

 for assessing temporal changes in the 

 abundance of these species (Penning- 

 ton, 1985; Helser and Hayes, 1995). 



Annual estimates of abundance de- 

 rived from fisheries-independent sur- 

 veys are typically regarded as provid- 

 ing a relative measure of population 

 abundance (i.e., they are indices of 

 abundance, not true estimates of to- 

 tal population size) (Grosslein, 1969; 

 Clark, 1979). Thus, the expected 

 value of the abundance index (e.g., 

 mean catch-per-tow for trawl surveys) 

 is regarded as proportional to the size 

 of the actual population, although the 

 constant of proportionality (the catch- 

 ability) is unknown. As such, rela- 

 tive changes in an abundance index 

 should reflect similar relative changes 

 in the actual population, and trends 



in the time series of such an index 

 should reflect similar trends in the 

 corresponding population. 



Unfortunately, abundance indices 

 derived from large-scale fishery-in- 

 dependent surveys typically exhibit 

 interannual variability much higher 

 than one would expect from within- 

 survey variance (Byrne et al., 1981; 

 Pennington, 1985). Part of the vari- 

 ability in such indices is presumably 

 due to the variability in the underly- 

 ing population — a variability that is 

 caused by population-dynamic pro- 

 cesses such as recruitment. However, 

 part of the variability is due to ob- 

 servation noise that arises from both 

 within-survey sampling variability 

 because of the heterogeneous distri- 

 bution of many fish stocks (Byrne et 

 al., 1981), and because of environmen- 

 tally driven factors that affect catch- 

 ability over time (Byrne et al., 1981; 

 Collie and Sissenwine, 1983). Low 

 signal-to-noise ratios in abundance 

 indices that are due to high observa- 

 tion noise reduce chances of detecting 

 important changes or trends in actual 

 population abundance. Variability due 

 to within-survey sampling can be re- 

 duced (before the fact) by adding more 

 stations to a survey, but additional 

 stations will not reduce variability 

 caused by changes in catchability. 



Time series modeling using autore- 

 gressive integrated moving average 

 (ARIMA; Box and Jenkins, 1976) 

 models provides an approach to re- 



