基于时序数据的CPI组合预测分析
Time-Series Data Based Composite Forecasting Analysis of CPI

居民消费价格指数(Consumer Price Index，简称为CPI)是客观反映消费品及服务价格的波动情况的一种宏观经济指标。CPI水平直接体现通货膨胀或紧缩状况，它在经济发展中起着重要作用，为政府制定宏观经济政策、规划经济市场业务以及分析货币或债券市场提供重要参考依据。因此，对CPI的预测分析研究具有重要现实意义。首先，采用三种单项模型，即自回归滑动平均求和(ARIMA)模型、最小二乘支持向量(LSSVM)回归模型和BP神经网络模型，分别对上海市2004年1月至2024年1月间的CPI月度数据进行拟合预测，并对单一模型预测误差进行比较分析。其次，建立两种组合模型对CPI进行预测分析。第一种由ARIMA模型和BP神经网络模型集成，此组合模型将居民消费价格指数时间序列分解为线性自相关主体和非线性残差两部分，利用ARIMA模型预测其线性主体部分，继而用BP神经网络模型预测其非线性残差部分，将两部分相加得到最终预测值。第二种将ARIMA模型和LSSVM回归模型进行赋权组合预测。最后，对比单一模型和不同组合模型的预测效果，从而找到优化的模型来对上海市CPI进行预测。研究发现，单一模型中ARIMA模型在其特定条件下表现出了最为出色的预测能力。而组合模型ARIMA-BP和ARIMA-LSSVM则各结合了两种模型的优点，使得其在复杂情况下的预测效果优于单一模型，其中ARIMA-BP模型优于ARIMA-LSSVM模型。总体上，ARIMA-BP模型预测表现最为卓越，预测结果最为准确。
The Consumer Price Index (CPI) is a macroeconomic indicator that objectively reflects the fluctuation of consumer goods and services prices. The level of CPI directly indicates inflation or deflation conditions, playing a crucial role in economic development by providing significant references for government policy-making, planning economic market operations, and analyzing monetary or bond markets. Therefore, research on forecasting analysis of CPI has substantial practical significance. Firstly, three single models—namely, the Autoregressive Integrated Moving Average (ARIMA) model, Least Squares Support Vector Machine (LSSVM) regression model, and Backpropagation (BP) Neural Network model—are employed to fit and forecast the monthly CPI data of Shanghai from January 2004 to January 2024. Comparative analysis of prediction errors among these single models is conducted. Secondly, two composite models are established for CPI forecasting. The first composite model integrates ARIMA and BP Neural Network models, decomposing the time series of the consumer price index into linear autocorrelation components and nonlinear residuals. The linear component is predicted using the ARIMA model, while the nonlinear residual part is predicted using the BP Neural Network model; their sum constitutes the final prediction value. The second composite model combines ARIMA with LSSVM through weighted forecasting. Finally, the forecasting effectiveness of single models versus different composite models is compared to identify the optimized model for predicting Shanghai’s CPI. The study found that among single models, the ARIMA model exhibited superior forecasting capability under specific conditions. Composite models ARIMA-BP and ARIMA-LSSVM each combine the advantages of two models,