基于多种预测模型的江西旅游需求的预测
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2011年7月23日
基于多种预测模型的江西旅游需求的预测
摘要
本文主要对江西省旅游需求的预测进行研究，收集近15年的相关数据，分别利用BP神经网络模型，灰色理论GM（1 1）模型，时间序列模型和多元线性回归分析模型进行预测，并运用平均相对误差（MAPE）参数来确定这几种模型对该问题预测的精确度，进行对比分析。最后，运用关联度分析法确定各因素的影响程度。
BP神经网络模型：本模型探讨用5-14-1三层BP神经网络模型来分析和预测江西旅游量。首先将1996～2010年间的样本数据归一化处理，利用ATLAB 神经网络工具箱进行模拟训练，建立了基于BP神经网络的旅游预测模型。
GM（1 1）模型：在分析灰色预测模型基本原理的基础上，利用MATLAB强大的矩阵功能，实现灰色预测GM(1,1)模型算法，并通过残差检验和关联度检验对该模型进行验证，预测江西未来五年旅游量。
多元线性回归分析模型：先将多个单因素分别与旅游量进行拟合，再将单因素确定的矩阵与旅游量通过matlab拟合，确定其为线性关系，故本问题可用回归模型预测。在得出旅游量与各因素的线性关系之后，通过各因素的值预测近20年的旅游量。
时间序列的趋势移动平均法模型：将1996~2010旅游量时间序列进行两次移动平均，利用移动平均滞后偏差的规律来建立直线趋势的预测模型，从而对江西未来5年的旅游量进行预测。
预测模型比较分析：本文借助平均相对误差（MAPE）参数对以上4种预测方法的预测结果进行分析比较 ,说明BP神经网络对江西旅游量的预测更加合理可行。
预测模型 MAPE
BP神经网络 0.000513
回归分析 0.013718
灰色理论 0.020357
时间序列 0.071849
关联分析：本文收集了1996~2010年江西每年的旅游量以及5个影响因素的时间序列资料。运用关联度分析法确定各因素的影响程度，按关联度大小排序为：全国居民人均可支配收入，江西省星级酒店数量，全国居民恩格尔系数，江西省商品零售价格指数，江西省高速公路里程。
关键词：旅游预测 BP神经网络 灰色理论GM（1，1） 多元线性回归分析 时间序列 关联度分析
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目录
1、问题重述 ································································································································· 3 2、模型假设 ································································································································· 3 3 符号说明 ································································································································· 3 4、问题分析 ································································································································· 4 5、预测模型建立与求解··········································································································· 4 5.1 收集数据 ············································································································ 4 5.2 基于BP神经网络的旅游预测模型 ·································································· 5 5.2.1 样本的选取································································································· 5 5.2.2 数据预归一化处理 ······················································································ 5 5.2.3 BP网络结构设计 ·························································································· 5 5.2.3 网络训练 ······································································································ 5 5.2.4 网络仿真模拟及数据还原 ·········································································· 6 5.2.5 网络预测 ······································································································ 6 5.2.6 模型检验 ······································································································ 7 5.3 灰色理论GM（1 1）模型 ·················································································· 8 5.3.1 背景知识 ······································································································ 8 5.3.2 GM（1,1）模型的建立················································································· 8 5.3.3检验和判断GM（1，1）模型的精度························································· 9 5.3.4模型求解与检验························································································ 10 5.3.5模型预测···································································································· 11 5.4 建立多元线性回归分析的模型 ······································································ 11 5.4.1 多元线性回归分析的模型的求解··························································· 12 5.5 时间序列的趋势移动平均法模型 ·································································· 14 5.5.1时间序列分析方法概述············································································ 14 5.5.2趋势移动平均法························································································ 15 6、模型对比分析 ······················································································································ 16 7、因素关联分析 ······················································································································ 16 关联分析法简介： ·································································································· 16 关联分析过程： ······································································································ 17 8、模型的评价与推广 ············································································································· 17 9、有关建议 ······························································································································· 18 参考文献 ······································································································································ 19 附录 ··············································································································································· 20
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1、问题重述
1.1问题背景：
随着社会的发展，旅游业已发展成为当今世界最大的经济产业；作为现代文明社会标志之一的旅游，也已成为现代人日常生活不可缺少的组成部分。
江西是旅游业发展速度最快的省市之一，具有丰富的旅游资源。 当前，江西省正在全面实施鄱阳湖生态经济区建设主战略。生态经济区建设强调的是绿色发展，而旅游业正是典型的绿色经济，因此可以说江西旅游业面临着非常难得的历史发展机遇，空间广阔，大有可为。因此对江西旅游需求的合理规划和正确预测，对促进江西旅游业的发展和文化交流有着十分重要的意义。 1.2需解决的问题：
（1）以江西省的旅游市场为研究对象，收集近15年的相关数据，建立3~4种定
量预测模型。
（2）结合若干性能评价指标对这3~4种模型进行对比分析。比较各模型的预测
效果。
（3）指出影响旅游需求的主要因素，向有关部门提出具体建议。
2、模型假设
（1）收集到的数据真实有效，客观的反应了江西旅游业的现状；
（2）假设旅游需求只与全国居民人均可支配收入，江西省星级酒店数量，全国居民恩格尔系数，江西省商品零售价格指数，江西省高速公路里程有关； （3）假设江西旅游业没有跳跃式发展，相对平稳；
（4）假设江西旅游业不受重大灾害（特大洪水，非典，猪流感）影响； （5）假设江西省旅游产业结构没有发生重大调整。
3、 符号说明
（1） Mt：一次平均移动值； （2）Mt(2)(1)：二次平均移动值；
（3）N：平均移动项数； （4）x(0):原始序列； （5）x（1）：累加序列； （6）y：旅游需求量
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4、问题分析
本文主要探讨的是对江西省旅游产业发展进行预测，并分析影响该旅游业的主要因素，及时向有关部门提出合理建议，推动江西省整个旅游产业的快速发展。
首先，打算收集从1996年到2010年与江西旅游业发展有关的数据，初步预计建立4种预测模型分别是：BP神经网络模型，灰色理论GM(1,1)模型，多元回归模型，时间序列模型。
其次,本文根据上述4种模型求解的结果以及运用平均相对误差法确定这4种模型的精确度，对比分析，找出最适合求解该类问题的模型并加以推广。
最后，初步选定用关联度分析法从若干个因素中筛选出对问题影响相对较大的因素并对剩下的因素进行排序，指出哪些因素主要影响旅游业发展，及时向有关部门提出合理建议。
5、预测模型建立与求解
5.1 收集数据
本文从江西统计年鉴和中国统计年鉴收集了1996年至2010年江西每年的旅游量和旅游收入以及5个影响因素的时间序列资料（见表1）。其中影响江西旅游量和旅游收入的5个因素为：全国居民人均可支配收入，江西省星级酒店数量，全国居民恩格尔系数，江西省商品零售价格指数，江西省高速公路里程。
表1 1996-2010年江西每年的旅游量和旅游收入及影响因素的时间序列资料
年份
旅游总人数 1309 1614 1620 2094 2537 2900 3270 3391 4089 5058 6000 6944 8100 9399.7 10815
旅游总收入 50.15 79.35 81.64 111.29 134.6 161.39 191.1 197.47 240.81 320.02 390.89 463.67 559.38 675.61 818.00
江西省星级酒店数量 91 92 110 124 136 142 140 140 145 147 186 190 200 215 243
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江西省高速公路里程 65 70 212 263 414 421 666 1040 1425 1559 1761 2206 2316 2433 3088
江西省商品零售价格指数 106.6 99.60 98.80 96.80 98.50 98.40 100.2 100.1 103.0 100.9 101.2 104.0 106.1 99.10 102.1
全国居民人均可支配收入 4838.90 5160.30 5425.10 5854.00 6280.00 6859.60 7702.80 8472.20 9421.60 10493.0 11759.5 13785.8 15780.7 17174.6 19109.0
全国居民恩格尔系数 48.80 46.60 44.70 42.10 39.40 38.20 37.70 37.10 37.70 36.70 35.80 36.30 37.90 36.50 35.70
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010