基于ARIMA与自适应过滤法的组合预测模型研究
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摘要
时间序列预测是根据已有的历史数据的变化趋势预测未来的发展,广泛应用于经济、环境、医疗等领域的预测。为了能有效提高时间序列预测的精度,提出一种集成自回归综合移动平均(ARIMA)模型与自适应过滤法的组合预测模型。该组合强调ARIMA模型对时间序列数据特征识别与参数估计的优势,同时引入自适应过滤法的"权数"调整思想,对ARIMA模型的参数进行调整,以减少预测误差,提高预测精度。从时间序列数据库(TSDL)中选取13组不同规模涵盖四类典型时间序列类型的算例分别对组合预测和传统的ARIMA预测进行对比。结果表明:对于所有算例的短期预测,组合预测的预测精度较ARIMA模型提高了80%～99%,预测相对误差(PE)的标准差减小了60%～90%,预测趋势更加接近实际情况。当预测步长加长时,ARIMA模型预测误差呈线性增加,而组合模型的预测精度的变化率基本维持不变,验证了组合模型长期预测的有效性。
Time series forecasting is to predict the future trend based on the variation trend of existing historical data,and is widely applied in several fields such as economy,environment,and healthcare. In this paper,a hybrid forecasting model based on the auto-regressive integrated moving average( ARIMA) model and the self-adaptive filtering method was presented to effectively improve the accuracy of time series prediction. It emphasized the advantage of ARIMA model for feature identification and parameter estimation of time series data. It also introduced the "weight"adjustment of the self-adaptive filtering method,and adjusted the parameters of ARIMA,so as to reduce forecast error and improve accuracy. We selected 13 sets of examples with different scales covering four types of typical time series from the time series data library( TSDL) to compare the forecasting result by the hybrid model and the ARIMA. Results show that compared with the ARIMA model,the prediction accuracy of the hybrid model increases by 80% to 99% and the standard deviation of the average relative error decreases by 60% to 90% for short-term forecasting. And the prediction tendency is closer to actual situation. When the prediction step lengthens,the prediction error of ARIMA model increases linearly,and the change rate of prediction accuracy of hybrid model remains nearly unchanged. It verifies the effectiveness of long-term forecasting of hybrid model.
Time series forecasting is to predict the future trend based on the variation trend of existing historical data,and is widely applied in several fields such as economy,environment,and healthcare. In this paper,a hybrid forecasting model based on the auto-regressive integrated moving average( ARIMA) model and the self-adaptive filtering method was presented to effectively improve the accuracy of time series prediction. It emphasized the advantage of ARIMA model for feature identification and parameter estimation of time series data. It also introduced the "weight"adjustment of the self-adaptive filtering method,and adjusted the parameters of ARIMA,so as to reduce forecast error and improve accuracy. We selected 13 sets of examples with different scales covering four types of typical time series from the time series data library( TSDL) to compare the forecasting result by the hybrid model and the ARIMA. Results show that compared with the ARIMA model,the prediction accuracy of the hybrid model increases by 80% to 99% and the standard deviation of the average relative error decreases by 60% to 90% for short-term forecasting. And the prediction tendency is closer to actual situation. When the prediction step lengthens,the prediction error of ARIMA model increases linearly,and the change rate of prediction accuracy of hybrid model remains nearly unchanged. It verifies the effectiveness of long-term forecasting of hybrid model.
引文
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[2] Lin Y,Yang Y. Stock markets forecasting based on fuzzy time series model[C]//IEEE International Conference on Intelligent Computing and Intelligent Systems. IEEE,2009:782-786.
[3] Sharma A, Mansotra V, Shastri S. Forecasting Public Healthcare Services in Jammu&Kashmir Using Time Series Data Mining[J]. International Journal of Computer Science&Software Engineering,2015,5(12):569-575.
[4] Wah W,Das S,Earnest A,et al. Time series analysis of demographic and temporal trends of tuberculosis in Singapore[J]. BMC Public Health,2014,14:1121.
[5] Medina D C,Findley S E,Guindo B,et al. Forecasting Non-Stationary Diarrhea,Acute Respiratory Infection,and Malaria Time-Series in Niono,Mali[J]. Plos One,2007,2(11):e1181.
[6]张美英,何杰.时间序列预测模型研究综述[J].数学的实践与认识,2011,41(18):189-195.
[7] Box G E P,Jenkins G. Time Series Analysis Forecasting and Control[M]//Time Series Analysis,Forecasting and Control. Holden-Day,1976.
[8]朱东妹.时间序列数据预测方法的应用研究[J].兰台世界,2011(10):73-74.
[9]周奎. ARIMA模型在我国GDP预测中的应用[J].广西职业技术学院学报,2016,9(1):19-23.
[10] Rahman A,Hasan M M. Modeling and Forecasting of Carbon Dioxide Emissions in Bangladesh Using Autoregressive Integrated Moving Average(ARIMA)Models[J]. Open Journal of Statistics,2017,7(4):560-566.
[11]张楠.时间序列预测法简介[J].经济与管理研究,1981(4):41-44,59.
[12]周雄鹏.自适应过滤法的原理、程序和应用[J].预测,1985(2):36-41.
[13]王坚强.自适应过滤法在经济预测中的应用[J].工业技术经济,1996,15(4):88-91.
[14]陶庭叶,高飞,吴兆福.自适应过滤法及其在大坝监测中的应用[J].测绘科学,2009,34(5):181-182.