基于多元回归分析的上证指数预测模型

1、上证指数预测模型摘要股票市场是我国资本市场的重要组成部分，在推动我国经济发展进程中起到了非常重要的作用。为了更好地理解股票市场以及获得更高的收益，股市的预测成了重多投资者和学术研究者研究和分析的热点问题。而上证指数是研究和判断股票价格变化趋势必不可少的重要依据,在一定程度上反映了我国的经济实力，是宏观经济的晴雨表，也是分析微观经济的重要指标，所以研究上证指数的预测模型具有非常重要的现实意义和使用价值。 本文在充分分析影响股市价格众多因素的基础上，选择多组变量，基于多元回归线性分析建立上证指数的预测模型。首先需要尽可能多的选择原始数据，在这里为了方便计算选择了3月到5月上证指数及各变量的数据（除

2、去休盘日）共64组，22个变量。使用SPSS软件进行线性分析后，剔除某些无关，甚至关联很小的变量后，得出了回归方程的系数，从而得出了上证指数的预测模型然后利用图表分析了此模型的好坏程度。关键词：1上证指数；2多元回归分析法；3 SPSS分析； 一、问题的背景与提出上证指数，是上海证券综合指数的简称。是最早发布的指数，以上海证券交易所挂牌上市的全部股票为计算范围，以发行量为权数的加权综合股价指数。它是研究和判断股票价格变化趋势必不可少的重要依据,在一定程度上反映了我国的经济实力，是宏观经济的晴雨表，也是分析微观经济的重要指标，所以研究上证指数的预测模型具有非常重要的现实意义和使用价值。本文将在此

3、背景下，充分分析上证指数的组成，使用多元线性回归的方法对其进行合理的预测，建立模型，具有实际意义，以预测未来上证指数的变化趋势。二、基本假设1. 忽略除文中提到的影响因素之外的因素对上证指数的影响。2. 假设经济形势稳定，不会出现较为明显的通货膨胀或通货紧缩。三、主要变量符号说明 为了便于描述问题，我们用一些符号来代替问题中涉及的一些基本变量，如表1所示。表1 主要变量符号说明一览表DIFFDEARSID指标J指标财政收入增长率财政支出增长率货币供应量货币流通量居民消费价格指数固定资产投资情况WRPSYOBV今日收盘价今日成交量昨日收盘价昨日成交量近5日平均收盘价近5日平均成交量近20日平均收

4、盘价近20日平均成交量【注】其余没有列出的符号，我们将在文章第一次出现时给出具体说明四、问题的分析 对上证指数进行预测，需要对影响上证指数的主要因素进行分析进行分析1：对整体股票市场而言，其状态最基本的表现方式是股票价格指数和成交量，而这两项指标又受社会、政治、经济、政策、心理等多种因素的影响。首先选择表中可以查到的数据作为变量：MACD:DIFF, DEA;RSI;KDJ:D指标,J指标;WR;PSY;OBV 其次选择以下变量：财政收入增长率、财政支出增长率、货币供应量、货币流通量、居民消费价格指数、固定资产投资情况。由于股民心理受收盘价和成交量的影响，故对上证指数的影响可用以下变量表示：今

5、日收盘价；今日成交量；昨日收盘价；昨日成交量；近5日平均收盘价；近5日平均成交量；近20日平均收盘价；近20日平均成交量. 以上均采用最近三个月的数据（包括上证指数）五、问题模型的建立和求解5.1问题的求解5.1.1多元线性回归分析的数学模型2设明日收盘价为y,影响因素为22个，分别为，,它们之间有以下线性关系5.1.2模型求解使用SPSS3进行回归分析得模型汇总模型RR 方调整 R 方标准 估计的误差1.997a.994.9916.97007a. 预测变量: (常量), x22, x17, x15, x18, x10, x5, x16, x14, x19, x20, x13, x4, x12

6、, x3, x9, x21, x2, x1, x11。模型平方和df均方FSig.1回归332809.2261917516.275360.552.000b残差2137.6024448.582总计334946.82863a. 因变量: yb. 预测变量: (常量), x22, x17, x15, x18, x10, x5, x16, x14, x19, x20, x13, x4, x12, x3, x9, x21, x2, x1, x11。系数a模型非标准化系数标准系数tSig.B标准 误差试用版1(常量)-774.86011619.193-.067.947x1.677.495.2911.368

7、.178x2-.703.423-.310-1.662.104x3-.230.323-.035-.712.480x4.180.239.048.754.455x5-.032.126-.014-.256.799x9-11.19519.037-.130-.588.559x1018.203121.877.031.149.882x11-21.96446.006-.144-.477.635x12-.019.120-.007-.157.876x13.387.238.0811.629.111x14-.258.687-.020-.376.709x15-.030.012-.058-2.582.013x16-4.82

8、4E-010.000-.040-1.759.086x17-.003.009-.006-.322.749x18-3.391E-010.000-.028-1.372.177x19-.017.030-.022-.561.578x202.887E-010.000.019.543.590x21.834.053.84615.595.000x221.800E-010.000.010.114.909a. 因变量: y5.1.3 模型结果6、 结果分析与进一步推广6.1多元线性回归分析结果图表从上图可以看出标准化残差的分布情况总体总体呈正态，集中在0的附近，这可以说明该回归方程的准确性是比较高的。由以上图表可知

9、较为精确与实际值接近。6.2预测模型准确情况分析在matlab中做出实际值与预测值的比较图如下七、模型的评价优点：1. 可推广性。该多元线性回归法可以应用到多变量线性关系问题评估中。2. 严谨性。SPSS与MATLAB相结合进行建模与模型评估，大大提高了模型的严谨性，较大程度的减少了人为计算可能会出现的误差。4. 全面性。变量的选择几乎涵盖了所有可能的影响因素，因此此建模过程是较为全面的。5. 实用性。本文所建模型与实际紧密联系，结合实际情况对数据进行合理的处理，使模型更加贴近实际，通用性强，具有现实意义。缺点：1. 由于时间的限制，对数据的统计和整理还不完善，其中读取数据量很大，有待进一步修

10、改。2. 由于选取变量的时间范围较窄，因此模型的准确性还有待在数据更多的条件下进一步的验证。八、参考文献：1 邹艳芬.上证指数的主要影响因素分析.江苏 连云港：连云港化工高等专科学校学报，2002.2 李金海.多元回归分析在预测中的应用.河北；河北工业大学学报，1996年第三期3 包凤达等.多元回归分析的软件求解与案例解读.数理统计与管理，2000年第五期附录一：变量数据表x1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20x21x22y-69.58-78.3540.452.868.456.515.422.14.499.610.768.0750

11、5082733.170 187207443002687.98207410709002842.82 255121888202898.68635224115526852914.92 -60.31-78.3550.0151.6344.286.515.422.14.499.610.728.5758.33520.782849.68 270961783002733.170 187207443002876.47 264376931802908.01945223903421952922.65 -51.55-78.3550.7553.6765.846.515.422.14.499.610.725.1558.33

12、513.652859.76 287478210002849.68 270961783002879.04 237980467402915.56765220873905352930.00 -42.95-78.3551.8857.5981.146.515.422.14.499.610.720.2858.33516.782874.17 312495169002859.76 287478210002868.04 219448031402922.7755217520667102937.30 -33.87-78.3553.7362.894.096.515.422.14.499.610.711.1866.67

13、518.952897.34 217466836002874.17 312495169002855.26 182398508402929.5433212223201952944.97 -26.06-78.3554.0768.44102.236.515.422.14.499.610.79.7975521.282901.39 233482661002897.34 217466836002847.70 177868347202937.3298214186377352953.52 -22.73-78.3550.2472.4496.466.515.422.14.499.610.721.0766.67519

14、.452862.56 138979461002901.39 233482661002840.29 163849148402944.78995214125346852962.15 -24.48-78.3545.0572.9375.86.515.422.14.499.610.739.2566.67518.062804.73 194816030002862.56 138979461002841.87 173351763202952.08315218222349102971.31 -25.12-78.3545.6471.562.996.515.422.14.499.610.737.2166.67519

15、.332810.31 127247554002804.73 194816030002861.89 174446599802961.09485217876779252981.13 -21.42-78.3550.7470.7966.556.515.422.14.499.610.721.5375521.282859.50 194816030002810.31 127247554002890.86 211663636002972.2775222515317752990.88 -17.88-78.3551.2369.9464.86.515.422.14.499.610.726.4875522.92286

16、4.37 163386667002859.50 194816030002922.72 243180517602980.48505221910449652999.18 -14.43-78.3551.8869.5967.536.515.422.14.499.610.729.7383.33524.782870.43 186492535002864.37 163386667002949.72 264578648602990.59865229241278603006.09 -8.81-78.3555.5871.5182.76.515.422.14.499.610.710.8983.33526.78290

17、4.83 200290213002870.43 186492535002977.62 270675634003001.19515230328543353010.70 -0.29-78.3560.4274.7493.556.515.422.14.499.610.78.2483.33529.922955.15 313332735002904.83 200290213002988.85 278018872003009.85955229794685253012.61 11.46-78.3565.678.53101.246.515.422.14.499.610.73.7283.33533.443018.

18、80 352400438002955.15 313332735002993.71 250367193803013.78605223293274103012.78 18.98-78.3562.8681.3498.26.515.422.14.499.610.711.3275530.742999.36 270377322003018.80 352400438002981.51 220291354403014.98695213499912203011.84 25.52-78.3563.7683.8699.016.515.422.14.499.610.77.1875532.913009.96 21697

19、7462002999.36 270377322002965.60 202808959003013.6478214138257053010.73 26.42-78.3556.8183.1979.156.515.422.14.499.610.726.3366.67530.542960.97 237006403003009.96 216977462002963.74 201487756803010.7943212759726403010.22 28.31-78.3558.6782.1575.936.515.422.14.499.610.723.4475532.292979.43 1750743440

20、02960.97 237006403002972.33 198169165203010.7078207769989653009.73 27.74-78.3555.6279.1861.326.515.422.14.499.610.733.8175530.272957.82 202021241002979.43 175074344002978.35 204463469603009.0696205309084603008.60 23.95-78.3550.5973.1236.86.515.422.14.499.610.762.366.67528.442919.83 182965345002957.8

21、2 202021241002997.40 215405290203009.4136201093602753006.93 27.16-78.3559.1670.9257.76.515.422.14.499.610.516.1766.67530.543000.65 210371451002919.83 182965345003023.55 225264631403011.1055198488717503004.58 29.62-78.3559.4770.9771.268.612.422.9699.810.519.8366.67532.753003.92 220413445003000.65 210

22、371451003025.11 227374242403008.35275194903308653001.36 31.66-78.3560.0472.9184.568.612.422.9699.810.515.2766.67534.813009.53 206545866003003.92 220413445003021.31 220872480003005.073189348167802988.74 36.37-78.3564.2976.4797.848.612.422.9699.810.52.866.67537.383053.07 256730344003009.53 20654586600

23、3026.20 223566971603000.7285187456056652975.24 39.44-78.3563.8780.01101.228.612.422.9699.810.55.9558.33535.063050.59 232262051003053.07 256730344003020.32 208764636402997.6385182889894752960.60 38.04-78.3556.9479.9979.858.612.422.9699.810.534.3350532.853008.42 220919506003050.59 232262051003023.53 2

24、24312875402995.001178518361352944.72 34.64-78.3553.4376.7357.178.612.422.9699.810.549.2750530.972984.96 187904633003008.42 220919506003038.31 221776540202945.2425177812210952927.05 35.48-78.3559.1775.8570.638.612.422.9699.810.572.9450533.173033.96 220018324002984.96 187904633003056.95 22211822380293

25、7.6177435895802916.78 34.92-78.3557.5464.6967.078.612.422.9699.810.524.6450531.343023.65 182718668003033.96 220018324003056.89 214775461402927.5315172476445102905.77 37.51-78.3562.2774.4673.68.612.422.9699.810.519.5850534.443066.64 310003246003023.65 182718668003060.72 209538367802918.20117013028500

26、2894.87 40.37-78.3563.8776.0685.718.612.422.9699.810.510.558.33536.523082.36 208237830003066.64 310003246003041.91 204166562402906.662161447005452883.48 41.81-78.3563.0877.8988.518.612.422.9699.810.513.5258.33534.633078.12 189613051003082.36 208237830003016.02 200400366202893.8995156751099452872.75

27、38.91-78.3555.277664.648.612.422.9699.810.546.4550532.793033.68 183304512003078.12 189613051002992.24 189920089602882.5365153003126502863.29 36.93-78.3556.4873.4157.868.612.422.9699.810.539.7550534.763042.82 156533200003033.68 183304512002974.84 178430435802873.0365150006354102854.95 29.36-78.3546.0

28、56835.598.612.422.9699.810.564.8541.67531.532972.58 283144219003042.82 156533200002959.22 170666116602861.271149204085402847.26 21.51-78.3543.5960.8117.678.612.422.9699.810.575.133.33529.032952.89 189406849002972.58 283144219002955.43 140210800802852.9875140626628002840.43 15.63-78.3544.635413.088.6

29、12.422.9699.810.571.7941.67531.012959.24 137211668002952.89 189406849002953.97 130062085802846.617136591330502833.94 9.84-78.3542.9247.347.648.612.422.9699.810.578.3441.67529.752946.67 125856243002959.24 137211668002949.79 124481877802840.8375135754269852827.48 6.63-78.3546.1542.7515.028.612.422.969

30、9.810.568.9550530.922964.70 117711604002946.67 125856243002944.98 133051357802834.5875135034079952821.02 3.16-78.3544.4738.8715.578.612.422.9699.810.573.741.67529.622953.67 130867640002964.70 117711604002950.30 142590458202827.107134324863002815.74 -0.24-78.3543.2235.7617.118.612.422.9699.810.578.07

31、41.67528.232945.59 138663274002953.67 130867640002959.13 145383206802820.5455132957844252810.04 -3.48-78.3542.0532.8615.468.612.422.9699.810.578.3133.33527.152938.32 109310628002945.59 138663274002772.66 159009851602814.3185131516971702803.44 -1.64-78.3552.534.3843.518.313.623.76.399.59.641.8541.275

32、28.822922.64 168703643002938.32 109310628002751.42 173223392002808.525131367419752807.19 -0.3-78.3552.2440.6978.548.313.623.76.399.59.642.7633.33527.172991.27 165407106002922.64 168703643002733.41 163648525402808.224133695254652812.11 1.29-78.3553.4449.25100.648.313.623.76.399.59.67.4741.67528.62299

33、7.84 144831383002991.27 165407106002702.57 157726197402798.59132026209842817.09 -4.24-78.3539.4847.6137.778.313.623.76.399.59.699.7733.33526.552013.25 206796498002997.84 144831383002670.17 156027451802787.520556131314811332823.95 -14.99-78.3531.0142.229.868.313.623.76.399.59.694.3733.33524.752832.11

34、 180378330002013.25 206796498002832.94 137532094202833.065882126874712122832.98 -23.2-78.3531.135.88-2.158.313.623.76.399.59.693.2641.67525.952832.59 120829310002832.11 180378330002836.69 124387146602833.125625123530736002832.99 -29.02-78.3532.0530.17-4.078.313.623.76.399.59.690.1341.67527.312837.04

35、 135795466002832.59 120829310002838.91 124895097402833.161333123710831072832.66 -33.34-78.3531.92277.998.313.623.76.399.59.675.5241.67525.952835.86 136337655002837.04 135795466002833.00 125833569402832.884286122847642862832.09 -37.04-78.3530.9324.8812.138.313.623.76.399.59.679.4533.33524.82827.11 11

36、4319710002835.86 136337655002827.21 120885052602832.655385121809949622832.08 -37.03-78.3536.7624.6423.188.313.623.76.399.59.668.841.67525.952850.86 114653592002827.11 114319710002826.89 119761290402833.1175122434136252832.76 -38.23-78.3515.7724.9126.568.313.623.76.399.59.672.0241.47524.722843.68 123

37、369064002850.86 114653592002825.45 120924663002831.504545123141458452833.65 -41.15-78.3531.1323.5815.588.313.623.76.399.59.688.1841.67523.312807.51 140487826002843.68 123369064002821.04 118541339202830.287123118697902834.66 -43.02-78.3531.0622.8518.748.313.623.76.399.59.688.4633.33522.22806.91 11159

38、5071002807.51 140487826002822.56 111149227002832.817778121188794782836.50 -42.51-78.3536.1126.246.328.313.623.76.399.59.661.541.67523.282825.48 108700899002806.91 111595071002825.67 109535665802836.05625122388010252839.07 -40.18-78.3540.7433.5577.638.313.623.76.399.59.621.0941.67524.492843.65 120470

39、455002825.48 108700899002824.78 109764650602837.567143124343311862842.53 -39.65-78.3537.1838.7770.078.313.623.76.399.59.648.8841.67523.372821.67 111452445002843.65 120470455002820.54 106934477402836.553333124988788002848.93 -39.3-78.3536.1541.5258.048.313.623.76.399.59.657.241.67522.342815.09 103527

40、265002821.67 111452445002839.53 127696056602839.53127696056602864.94 -38-78.3538.2443.9558.548.313.623.76.399.59.647.6141.67523.492822.44 103527265002815.09 103527265002845.64 133738254502845.64133738254502871.29 -36.66-78.3537.9845.7756.718.313.623.76.399.59.649.3733.23522.392821.05 109845823002822.44 103527265002853.37 143808584332853.373333143808584332879.84 -30.07-78.3538.4448.3864