空气污染指数的分形结构和其趋势预测研究.pdf

空气污染指数的分形结构及其趋势预测研究 ——以大连市空气环境为例 东北财经大学 连祥斌、李峤志、周洋 摘要 随着生活水平的提高，人们越来越关心空气环境质量状况。本文利用R/S 分析非参数统 计方法，对大连市空气污染指数的分形结构进行了实证研究。首先介绍分形的概念及其描述 方法，考察大连市空气污染指数的分形特征，然后利用R/S 分析的两种形式确定大连市空气 污染指数的平均循环周期。在此基础上，利用经验法则估计大连市空气污染指数的每日动态 Hurst 指数，并计算7 日移动平均Hurst 指数。最后利用Hurst 指数及其7 日移动平均设计了 一种趋势预测方法，并通过对历史数据追溯预测检验了模型的预测效果。研究结果表明，大 连市空气污染指数具有分形结构，它的平均循环周期为7 天，即具有平均为7 天的记忆长度。 动态Hurst 指数和移动平均Hurst 指数对大连市空气污染指数的趋势具有一定的预测能力，尤 其是当其靠近1 或0 时的预测效果非常好。 关键词：分形；空气污染指数；R/S 分析法；Hurst 指数 i Abstract In the wake of the rapid development of human life level, the living conditions, especially air pollution have aroused more concern among our citizens. So the authors of this paper try to combine the non-parametric method—R/S analysis with the study of fractal structure on the Air Pollution in Dalian. To begin with, we give a fundamental introduction of fractal and its description method. In order to determine the average cycle of the Air Pollution in Dalian, we apply two forms of R/S analysis, which provides a basic way to calculate the dynamic Hurst index and the moving average Hurst exponent. Finally, the author makes perditions and compares the result with reality with the help of history data. Our research shows that the Air Pollution Index in Dalian does has fractal structure with an average cycle of seven days, that is to say, the index keeps the memory of the past seven days on average. The dynamic Hurst index and the moving average Hurst index can specifically and precisely predict the Air Pollution Index in Dalian, especially in the case that they are close to 1 or 0. Key words: fractal; Air Pollution Index; R/S analysis; Hurst Index 一、引言 一个成年人每天呼吸2 万多次，吸入空气20 公斤左右，比一天摄入的食物和水分多 10 倍多。人不摄食存活时间为20 天，不摄入水分存活时间为7 天，不