对采购经理人指数的一个分析——基于时间序列和神经网络模型

Analysis of Purchasing Managers Index( PMI) Based on Time Series and Neural Network Model

采购经理人指数(PMI)是经济活动扩张与收缩的晴雨表,PMI指数已经广泛应用于政策制定、企业决策和经济分析过程,但关于采购经理人指数自身变化规律的研究仍比较少见。本文以国家统计局、物流联合会(CFLP)和汇丰银行(HSBC)采购经理人指数的历史数据为研究对象,分析其波动规律、数据差异及经济意义。由于宏观经济政策发挥作用具有较长时滞,增强对经济波动的预见具有较大的应用前景。本文采用多种模型对各PMI数据序列进行拟合与预测,包括简单ARIMA模型、疏系数模型、乘积季节模型和神经网络模型,通过协整检验验证了CFLP和HSBC制造业采购经理人指数之间的协整关系。预测结果显示,除疏系数模型误差超过3%外,各模型预测误差均低于2%。本文结论指出,不同PMI指数存在明显数据分布特征差异,这种差异具有明显经济意义;我国采购经理人指数临界点、趋势和波动能够较好地反映宏观经济变动。我国的临界点含义与发达国家不同,临界值53.79能够反映经济增长率的转折点,而PMI长期趋势则与我国潜在实际经济增长率的趋势相吻合;在短期预测中,乘积季节模型、神经网络模型及ARIMA模型预测的表现优于疏系数模型,能够较好地判断短期经济走势。其中,乘积季节模型与简单ARIMA模型不同,可以提取时间序列趋势效应和季节效应、随机波动之间的复杂关系。本文最后提出建议,包括采用各种方法加强采购经理人指数预测、分析不同赋权方法、优化PMI指数季节调整与抽样方法、设计行业指数并拓展其应用范围,以便更好地为宏观经济政策和企业决策制定提供参考。

Purchasing managers＇ data has been widely used in policy- index （PMI） making is a barometer of economic activity expansion and contraction. PMI , enterprise decision-making and economic analysis, but that the research on change rule of the purchasing managers＇ index itself is still very rare. Basing on the history data of manufacture PMI from National Bureau of statistics of China and China Federation of Logistics ＆ Purchasing （CFLP） ,and HSBC, we analyze its variation rule, data gap and economic significance. Due to macroeconomic policy＇ s long time delay, there is great significance to enhance prediction about the economic fluctuation. This article uses many kinds of model for fitting and forecasting, including simple ARIMA model, Sparse Coefficient model, Muhiplicative Seasonal model and Neural Network model. We verified the data by means of cointegration test. Prediction results showed that except the Sparse Coefficient model＇ s error more than 3% , all others＇ prediction error is less than 2%. The major conclusions and suggestions as below： （1） There is slight trend in CFLP and HSBC PMI data, while the CFLP non-manufacturing PMI has obvious seasonal fluctuations,such as in February and April each year, appear high and low point respectively. CFLP and HSBC PMI have consistent basic direction, and in November 2008, three indexes hitting low record. However, a few partial discrepancies exist. （2） The mean of Non-manufacturing PMI data is much higher than the manufacturing, partly reflected the 2008-2012＇ s characteristic, non-manufacturing industries including the real estate industry, aviation, architecture and so on, face to better circumstance and receive higher development opportunities. Higher fluctuation of Non-man- ufacturing PMI data appear. On the one hand, the volatility comes from the seasonal factor. Non-manufacturing busi- nesses such as airlines, restaurants, retail will be variable with the seasons. On the other hand, the orders are more vulnerable to economic fluctuations. Standard deviation of CFLP is slightly less than HSBC, which may be partially due to the enterprise scale difference. Three groups of PMI data showed a peak distribution, but that HSBC PMI is relatively flat. CFLP - PMI index of 53 and 54 interval frequency is above 22% , according to the critical point with the GDP growth rate of 53.79. We can infer that macroeconomic stable growth interval accounted for more than 22% , and that speed up period range of more than 20%. Three set of indexes are negative skewness, but that the CFLP appear relative apparent, showing all have individual extreme low, namely presenting that the probability about 2% of poor economic conditions. The extreme good economic situation＇ s probability is normal. Which reflects an u- niversal law, namely ＂the difficult economy is different, but the period of economic prosperity is mostly similar＂ ~ Manufacturing PMI boom appears relatively high probability. （3） In United States, the use of the PMI for overall economy, focusing on two critical values of 42. 6 and 50. For China＇s economic growth rate is higher,we found that GDP annual growth rate of the critical value is about 53.79,if the manufacturing PMI in 53.79 above for some time, annual GDP growth rate will rise, otherwise will be fall. In addition to the critical point, we usually tend to ignore the relationship between PMI trends and GDP. We can discover that PMI index trend and potential real GDP growth rate is close related. （4） In the prediction process, we should choose suitable model according the basis of different series of PMI. We discover that in the short-term forecasting, Multiplicative Seasonal model, Neural Network model and sim- ple ARIMA model will play better than Sparse Coefficient model. Both simple ARIMA model, Sparse Coefficient model, Multiplicative Seasonal model and Neural Network model can reach the error level of less than 4% ,in addi- tion to the sparse coefficient model error receiver 3.5% , with that Neural Network model and ARIMA model of sin- gle-step prediction error is less than 1% , Multiplicative Seasonal is 1.46%. （ 5 ） Strengthen the analysis of the PMI index forecast, we can provide a reference for macroeconomic policies in a timely manner. Further should be aimed at the PMI diffusion index and industry index prediction research. Study the relationship between PMI and the economic growth of different industries will be more significance. Weighting approach for the PMI composite index should be analyzed. The relationship between economic growth and different weighting PMI is worth to dive in. Better seasonally adjust and sampling method will be further arriving at. In addi- tion, we should explore and improve the structure of the PMI index sampling scope, sampling method, to further im- prove the data quality. Only though these methods can we better service for the national macroeconomic regulation and business policy decisions.