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## Forecasting the catch of kilka species (Clupeonella spp.) using Time Series SARIMA models in the Southern Caspian Sea | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Caspian Journal of Environmental Sciences | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مقاله 4، دوره 16، شماره 4، زمستان 2018، صفحه 349-358
اصل مقاله (975 K)
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نوع مقاله: Research Paper | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

شناسه دیجیتال (DOI): 10.22124/cjes.2018.3203 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نویسندگان | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

K Amiri^{1}؛ N Shabanipour^{2}؛ S Eagderi^{3}
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^{1}Department of Biology, Faculty of Science, University of Guilan, Rasht, Iran | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{2}Department of Marine Sciences, The Caspian Sea Basin Research Centre, University of Guilan, Rasht, Iran | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{3}Department of Fisheries, Faculty of Natural Resources, University of Tehran, Karaj, Iran | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Fisheries management receives assistance by prediction of events to evaluate fluctuating values for a target species to formulate proper policies and actions particularly for threatened and endangered species. This study aimed to predict 7 years Catch Per Unit Effort (CPUE) of kilka fishes as at-risk population in southern regions of the Caspian Sea. The former catch data from the Fisheries Organization of Iran (IFO) archives (1997 to 2014) were analyzed using ARIMA and SARIMA models. The data were divided into four parts (quarters) addressing one-fourth of a year to represent time and expressed as “Q”. According to periodic changes of ACF and PACF indices, seasonal ARIMA (SARIMA) models were used. The appropriate SARIMA models were examined using BIC, RMSE, R2, MSE and Ljung-Box indices. SARIMA (0, 1, 1) × (0, 1, 1) 4 process was the selected final model which met the criterion of model parsimony according to BIC of 31.91, RMSE of 7195193 , MAE of 4372178 , R2 of 0.82 and Ljung-Box index < 0.05. Based on selected SARIMA model, the forecasts indicated that if the fishing fleet and efforts remain at the present level, the performance of kilka fishing will likely have gentle rise by 2021. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژهها | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

SARIMA model؛ Kilka؛ Time series forecasting؛ Fishing effort؛ South Caspian Sea | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

اصل مقاله | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

*, Eagderi S.^{3}
Fisheries management receives assistance by prediction of events to evaluate fluctuating values for a target species to formulate proper policies and actions particularly for threatened and endangered species. This study aimed to predict 7 years Catch Per Unit Effort (CPUE) of kilka fishes as at-risk population in southern regions of the Caspian Sea. The former catch data from the Fisheries Organization of Iran (IFO) archives (1997 to 2014) were analyzed using ARIMA and SARIMA models. The data were divided into four parts (quarters) addressing one-fourth of a year to represent time and expressed as “Q”. According to periodic changes of ACF and PACF indices, seasonal ARIMA (SARIMA) models were used. The appropriate SARIMA models were examined using BIC, RMSE, R2, MSE and Ljung-Box indices. SARIMA (0, 1, 1) × (0, 1, 1) 4 process was the selected final model which met the criterion of model parsimony according to BIC of 31.91, RMSE of 7195193 , MAE of 4372178 , R2 of 0.82 and Ljung-Box index < 0.05. Based on selected SARIMA model, the forecasts indicated that if the fishing fleet and efforts remain at the present level, the performance of kilka fishing will likely have gentle rise by 2021.
The Caspian Sea (36° to 47° N and 46° to 54° E) is a landlocked body of water on the Euro-Asian continent. Modern autochthonous Caspian fauna evolved from limited number of marine species since 1.8 million years ago as an isolated brackish water body without competition enforcement by marine species (Karpinsky 2002). The Caspian Sea kilka group ( Over the past two decades, the species composition on one part and density of the Caspian Kilka on the other part have been negatively changed (Karimzadeh Forecasting based on historical time series data, has become an efficient tool for future fisheries planning. Efficient models can provide accurate operational forecasts of annual commercial landings in coastal waters (Stergiou & Christou 1996). Planners can predict commercial landings for the next year and season using time series approaches where the data are updated periodically (Czerwinski Therefore, the present study tried to forecast the monthly and also seasonal CPUE (Catch Per Unit Effort) of the kilka fishes in the southern part of the Caspian Sea employing SARIMA model. The efficiency of the forecasting techniques applicable to the Caspian fisheries was discussed.
The analyses were based on the daily CPUE data obtained from fishing vessels during 1997 to 2014 at two main Kilka fishing areas in the southern part of the Caspian Sea i.e. Anzali (37°28'N,49°25'E) and Babolsar (36°42′N, 52°39′ E) ports (Fig. 1). CPUE is calculated as the catch divided by the effort. The CPUE data collected by the Iranian Fisheries Organization (IFO) were divided by four quarters. A quarter refers to one-fourth of a year and is typically expressed as "Q”. The four quarters that made the year were: March to June (Q1); June to September (Q2); September to December (Q3); December to March (Q4) representing four seasons in Iran. CPUE of kilka ranged between 93802 kg to 14239979 kg, reaching its highest value of 30993544 kg in winter (Q4) of 1998 and falling to 93802 kg in spring (Q1) of 2014.
Box and Jenkins (1976) presented Seasonal Autoregressive Integrated Moving Average (SARIMA) of a time series model as (1):
Where X If q = 0 then (1) is an autoregressive model of order p, denoted by AR (p). If p = 0 the model is a moving average model of order q, denoted by MA (q). Model (2) may be put as:
A(L) X_t=B(L)ε_t
where A(L) = 1 - α 1`L - α 2L2 - … - αp Lp and B(L) = 1 + β 1L + β 2L2 + … + β qLq and LkXt = Xt-k. A (L) and B (L) are the autoregressive (AR) operator and the moving average (MA) operator respectively.
If the time series {X
where s is the seasonality period, (L) = 1+
stationary and invertible.
A test of stationary (or non – stationary) that has become widely popular over the past several years is the unit root test. This is the test that is used to carry out or to know the order of integration. It is important to know the order of integration of non-stationary variables, so they may be different before being included in a regression equation. The most common unit root tests are ADF test (Dicky & Fuller 1979).
Ljung and Box (1978) proposed a Q-Test called Ljung–Box test which is commonly used in linear models following Box-Jenkins methodology. This test is applied to the residuals of a fitted model, not the original series, and in such applications the hypothesis to be tested is that the residuals from the model have no autocorrelation. Perhaps it performs a lack-of-fit hypothesis test for model misspecification based on the
Where N = sample size, L = number of autocorrelation lags included in the statistic, and p
First, the stationary and seasonality have been addressed, and then the order (the p and q) of the autoregressive and moving average terms were found. The primary tools for doing so are the autocorrelation plot and the partial autocorrelation plot. However, according to Box & Jenkins (1976) the model should be parsimonious, having as few parameters as possible and fulfill all the diagnostic checks. The BIC, RMSE, MAE, R-square, and Ljung-Box test suggested that the parsimony criteria of the model building as information criteria for the purpose of selecting an optional model fits to a given data. Also the model adequacy by examining the sample autocorrelation as function of the residual (ACF) and the sample partial autocorrelation as function of the residual (PACF) was checked. We can conclude that the model is adequate if there are no spikes in the ACF and PACF.
The first step in developing a Box-Jenkins model is to determine if the series are stationary. So that, Root test of stationary ADF was carried out. The The ACF had spikes of multiple of 4, 8, 12, 16, 20 and 24 (Fig. 3 a, b and c)), indicating that seasonal differencing was necessary. The seasonal difference on the stationed quarterly series (ADF test
Nine candidate models were selected (Table 1). The best model was found as SARIMA (0, 1, 1) × (0, 1, 1) The Ljung-Box statistic indicated that there was no significant departure from white noise for the residuals as the The bounded dash line shows 80% (lower line) and 95% (upper line) prediction intervals respectively.
* = Best model
This study aimed to identify a time series model to forecast the kilka CPUE in the southern part of the Caspian Sea from 1997 to 2014 employing of Box-Jenkins fundamental approach. The model was developed in three stages. In the first stage, the model was identified, where the series was not non stationary at level form based on the result provided by ADF test, correlogram and time plot. It was found out that the series was stationary at the 1 seasonal difference was made due to significant spikes at certain lags of the quarterly stationary series. Based on simultaneous criteria selection for BIC and RMSE, SARIMA (0, 1, 1) × (0, 1, 1) Then, CPUE was forecasted indicating that the kilka CPUE will have gentle rise by 2021 (Table. 3; Fig. 6). The forecast indicated that in current fishing effort, the CPUE of southern part of the Caspian Sea kilka will be almost stable for few coming years ahead and the present seasonal condition will be retained. In addition, the first difference ACF correlogram showed that Q4 fishing season in Iran established the key role in kilka CPUE fluctuations.
We would like to thank Fisheries Statistics and Economy Group of Iran Fisheries Organization especial Sabah Khorshidi for providing the data, which has been used in this study. The authors wish to thank Ette Etuk (Rivers state University, Nigeria) and Hadi Poorbagher (University of Tehran) for their review and scientific guidance. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مراجع | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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