Application of time series analysis model on stock prediction of small yellow croaker (Larimichthys polyactis) in the southern Yellow Sea
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摘要: 本文选取2003−2014年黄海南部帆式张网小黄鱼渔获量的监测数据,运用时间序列分析模型ARIMA (1,2,0)进行拟合及预测,并用2015−2016年小黄鱼年单位捕捞努力量渔获量值进行验证。结果显示,2003−2014年的小黄鱼年单位捕捞努力量渔获量模拟值与真实值接近,相关系数为0.881 (p<0.05),相关性显著;2015年和2016年预测值分别为47.66 kg/网和49.16 kg/网,与实际值(51.10 kg/网和40.05 kg/网)相对误差分别为6.73%和22.75%,总体相对误差为14.74%。表明ARIMA (1,2,0)模型对黄海南部小黄鱼渔获量时间序列的变化趋势进行拟合和预测是可行的,在短期预测方面更具优势。不同时间序列数据ARIMA模型的p、d、q值不尽一致,在数据分析时不能简单地套用固定模型,应根据相关理论指导和分析,确定适宜的p、d、q值。Abstract: In this paper, the time series analysis model ARIMA (1, 2, 0) was applied to simulate and predict the stock of small yellow croaker (Larimichthys polyactis) based on the monitoring catches data of canvas stow net in the southern Yellow Sea from 2003 to 2014 and verified by the monitoring catches data of 2015 and 2016. The results showed that the simulated and actual values for the catch yield from 2003 to 2014 were correlated significantly (p<0.05) and the correlation coefficient was 0.881. The relative error between predicted and actual value in 2015 and 2016 were respectively 6.73% and 22.75%, the overall relative error was 14.74% and the regression equation fitted the real situation better, which illustrated that the time series analysis model ARIMA (1, 2, 0) can be applied to simulate the catches trend of L. polyactis and predict the catch stock, especially superior in short-term forecasting. However, in any case the fixed model of L. polyactis is not always suitable for all data analysis, and the values of p, d and q in ARIMA model are considered to be variable according to different time series. Therefore, the optimal values of p, d and q should be determined based on the guidance and analysis of relevant theories in order to avoid copying directly the fixed model.
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Key words:
- small yellow croaker /
- stock /
- time series analysis /
- ARIMA model /
- the southern Yellow Sea
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表 1 2003−2016年黄海南部帆式张网监测船数、航次数和总投网次数
Tab. 1 The number of monitoring vessel by canvas stow net, voyage and hauls from 2003 to 2016 in the southern Yellow Sea
年份 监测渔船数量/艘 航次数/次 总投网次数/网 2003 2 34 1 908 2004 2 25 1 897 2005 2 31 1 749 2006 2 30 1 722 2007 2 31 2 015 2008 2 32 2 202 2009 2 32 2 012 2010 2 35 2 005 2011 2 30 2 756 2012 4 34 2 268 2013 2 32 1 502 2014 2 32 3 035 2015 3 37 3 422 2016 2 36 2 892 表 2 4类模型的相关函数性质
Tab. 2 The correlation function properties of four types of models
模型系数 AR (p) MA (q) ARMA (p,q) ARIMA (p,d,q) ACF 拖尾 q阶截尾 拖尾 非平稳时间序列 PACF p阶截尾 拖尾 拖尾 表 3 水平序列和差分序列单位根检验表
Tab. 3 Unit root test of horizontal sequence and difference sequence
数据处理 单位根检验 1%显著水平 5%显著水平 10%显著水平 水平序列 −2.766 2 −4.200 1 −3.175 4 −2.729 0 一阶差分序列 −4.337 7 −4.297 1 −3.212 7 −2.747 7 二阶差分序列 −6.318 4 −4.420 6 −3.259 8 −2.771 1 表 4 ARIMA(1,2,0)模型参数估计表
Tab. 4 The parameter estimation of the ARIMA (1, 2, 0) model
模型 参数 估计值 标准误 ARIMA(1,2,0) AR1 −1.006 2.969 常数项 −0.714 0.246 -
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