Abstract:

A prediction method utilizing ARIMA based on spatio-temporal Multiple Linear Regression（MLR） is proposed, referring to the problems of ignoring space influence and space-time interaction in traditional time series modeling and prediction. The method is applied to spatio-temporal prediction of monthly average temperature in Liaoning Province. Firstly, the obvious seasonality existing in the space-time variable is removed by time series decomposition. Secondly, the MLR model for the Seasonality-Removed Data（SRD） is fitted by all-subsets regression method, in order to obtain the space-time trend in the SRD. Thirdly, an ARIMA model is fitted for the random data of each station. Finally, the space-time estimations are composed of the random estimations and other ones of first two steps. The experimental results show that the correlation coefficient between estimation and observation values is 0.993 4 and the mean absolute error is about 0.9 ℃.

Key words: spatio-temporal prediction, ARIMA model, Multiple Linear Regression（MLR）

摘要：

针对传统时间序列建模预测过程中忽略空间因素影响和时空交互的问题，提出了一种基于时空多元回归（MLR）的ARIMA预测方法，并应用于某省月均气温的时空预测研究中。通过时序分解去除时空变量明显的季节变化；运用全子集回归法确定显著影响气温的因素，继而得到去季节项数据的MLR模型，从而去除气温的时空趋势变化得到随机变化项；对各站点的随机项时间序列分别进行ARIMA建模；将随机项的预测值与前两项预测值重组，获得最终各站点的时空预测值。实验结果表明，预测值与观测值整体相关系数为0.993 4，误差绝对值均值约为0.9 ℃。

关键词: 时空预测, 差分自回归移动平均（ARIMA）模型, 多元线性回归（MLR）