Time Series Modelling of the Caspian Kutum (Rutilus frisii) Catch Using SARIMA Model

The Caspian Kutum (Rutilus frisii) is one of the most important bony fish speciesof the Caspian Sea and has high conservation and commercial value. There were decreasingtrends in its catch levels in the last years. Identifying temporal trends of its catch could helpadopt proper plans to maintain the stocks of this important species and achieve sustainableexploitation goals. In the present study, we conducted a time-series analysis for catch data ofthe species over a decadal period.

The commercial catch data of Caspian Kutum, over the seine netfishing points of the northern coastal regions of Iran during catch seasons 2002/03 to 2011/12,were used as catch-per-unit-of-effort (CPUE). A 5-point moving average of CPUE was used todistinguish the fishing points as optimum (with normalized CPUEs ≥ 0.6) and non-optimum(with normalized CPUEs < 0.6) fishing locations. Time series modeling was conducted usingthe seasonal autoregressive integrated moving average (SARIMA) model based on seasonal 3-month intervals. The performance and predictive ability of the models were assessed using aset of indices, including Akaike’s information criteria (AIC), Bayesian information criterion(BIC), root mean squared error (RMSE), normalized root mean squared error (nRMSE), meanabsolute error (MAE), normalized mean absolute error (nMAE) and the Pearson correlationcoefficient (r). CPUE trends over the five years of 2013 to 2017 were predicted using the bestfittedSARIMA models.

Five optimum (HR) and six non-optimum ranges (CR) were identifiedover the whole fishing points range (WR). The fitted SARIMA models based on the whole dataof all fishing locations as well as classified optimum and non-optimum ranges of fishinglocations did not have significant non-seasonal autoregressive and moving averagecomponents, indicating no increasing nor decreasing trends for CPUE over the study period,while for some of the ranges of fishing points, there were significant autoregressive and movingaverage components with clear seasonal increasing trends. The overall trend of CPUEs showedmainly an increase from 2002 to 2006, and then after relatively constant levels, there weredecreases from 2009 to 2013. The obtained predictions from the models for data sets havingsudden temporal fluctuations were less accurate. In contrast, higher accuracy levels ofpredictions and trends were observed for fish catch time series with no sudden alterations inCPUE levels over the studied period. Most of the obtained predictions for 2013-2017 similarlypresented stationary fluctuation trends with apparent seasonal increases in CPUEs.

Time-series modeling for R. frisii using the SARIMA method mainly indicatedclear increasing seasonal trends without any general trend of change over the whole fishingpoints. The simplicity of the obtained models considering the obtained seasonal and nonseasonalcomponents could be explained by the short time frame and the low number of datapoints. However, spatial classification of fishing points resulted in more detailed models andhigher recognition potential of them. The findings of this research could lead to a betterunderstanding of the temporal trends in catch levels of Caspian Kutum and use them by fisheriesmanagers to adopt efficient management plans regarding the available stocks of this species inthe future.