基于BP滤波的Fourier模型在粮食产量预测中的应用

本文尝试将经济学中的功率谱分析（BP滤波）与统计学中的Fourier模型相结合，先利用BP滤波选出对气候产量波动影响较大的周期，再对这些周期建立Fourier模型来拟合气候产量；同时运用多项式模型拟合趋势产量，并用滞后模型对残差进行修正，以提高粮食单产预测的精确度。利用1961-2000年粮食单产序列数据，分别采用Fourier方法和多项式滞后方法、BPNN法和灰色模型法建立模型，以2001-2012年粮食单产数据进行拟合检验。将这3种方法拟合结果进行比较。结果表明，本文引入的模型通过0.01水平的显著性检验且相对误差均在5%以下，利用模型对粮食单产进行中长期预测的结果表明，2013-2017年中国粮食单产将稳定在6018.6～6466.7kg·hm?2。BP神经网络法模拟的粮食单产虽然拟合相对误差较小，但模型不能得到直观解释，在预测时存在一定的随机性；灰色模型模拟的粮食单产相对误差高达35%，与实际产量存在较大差异。研究结果反映出Fourier模型和多项式滞后模型在粮食产量预测中，其精确度更高且更直观，能够用以预测未来粮食单产以及未来气候变化对粮食单产的影响。

Application of Fourier Model Based on BP Filter in Crops Yield Prediction

In order to improve the accuracy of yield prediction, we attempted to combine the power spectrum analysis (BP filter) in economics and the Fourier model in statistics, by using BP filter to choose the cycle, which had a great impact on the climate yield fluctuation, and established Fourier model to predict the climatic yield. At the same time, by using polynomial to predict the trend yield and the lag model to correct the residual. Grain yield data from 1961 to 2000 was taken as training data, by using three methods, Fourier method and polynomial lag method, BP neural network and grey model to construct the equations, and grain yield from 2001 to 2012 was used to test the three models. The three methods were compared by the fitting results. The results showed that the model was significant and the relative errors were all less than 5%. The predicted grain yields according to this model were at 6018.6-6466.7kg·ha?1 from 2013 to 2017. Meanwhile, the relative errors by BPNN were small, but the model could not be explained intuitively. The relative errors by the grey model reached up to 35%, it existed large differences with the actual yield. The results indicated that, in terms of predicting the grain yield, the Fourier model based on BP filter and the polynomial lag model had higher prediction accuracy and was more intuitive, which could not only predict the future grain yield, but also predict the impact of the future climate change on the grain yield.