基于多元回歸分析的上證指數(shù)預測模型

1、上證指數(shù)預測模型摘要股票市場是我國資本市場的重要組成部分，在推動我國經濟發(fā)展進程中起到了非常重要的作用。為了更好地理解股票市場以及獲得更高的收益，股市的預測成了重多投資者和學術研究者研究和分析的熱點問題。而上證指數(shù)是研究和判斷股票價格變化趨勢必不可少的重要依據,在一定程度上反映了我國的經濟實力，是宏觀經濟的晴雨表，也是分析微觀經濟的重要指標，所以研究上證指數(shù)的預測模型具有非常重要的現(xiàn)實意義和使用價值。 本文在充分分析影響股市價格眾多因素的基礎上，選擇多組變量，基于多元回歸線性分析建立上證指數(shù)的預測模型。首先需要盡可能多的選擇原始數(shù)據，在這里為了方便計算選擇了3月到5月上證指數(shù)及各變量的數(shù)據（除

2、去休盤日）共64組，22個變量。使用SPSS軟件進行線性分析后，剔除某些無關，甚至關聯(lián)很小的變量后，得出了回歸方程的系數(shù)，從而得出了上證指數(shù)的預測模型然后利用圖表分析了此模型的好壞程度。關鍵詞：1上證指數(shù)；2多元回歸分析法；3 SPSS分析； 一、問題的背景與提出上證指數(shù)，是上海證券綜合指數(shù)的簡稱。是最早發(fā)布的指數(shù)，以上海證券交易所掛牌上市的全部股票為計算范圍，以發(fā)行量為權數(shù)的加權綜合股價指數(shù)。它是研究和判斷股票價格變化趨勢必不可少的重要依據,在一定程度上反映了我國的經濟實力，是宏觀經濟的晴雨表，也是分析微觀經濟的重要指標，所以研究上證指數(shù)的預測模型具有非常重要的現(xiàn)實意義和使用價值。本文將在此

3、背景下，充分分析上證指數(shù)的組成，使用多元線性回歸的方法對其進行合理的預測，建立模型，具有實際意義，以預測未來上證指數(shù)的變化趨勢。二、基本假設1. 忽略除文中提到的影響因素之外的因素對上證指數(shù)的影響。2. 假設經濟形勢穩(wěn)定，不會出現(xiàn)較為明顯的通貨膨脹或通貨緊縮。三、主要變量符號說明 為了便于描述問題，我們用一些符號來代替問題中涉及的一些基本變量，如表1所示。表1 主要變量符號說明一覽表DIFFDEARSID指標J指標財政收入增長率財政支出增長率貨幣供應量貨幣流通量居民消費價格指數(shù)固定資產投資情況WRPSYOBV今日收盤價今日成交量昨日收盤價昨日成交量近5日平均收盤價近5日平均成交量近20日平均收

4、盤價近20日平均成交量【注】其余沒有列出的符號，我們將在文章第一次出現(xiàn)時給出具體說明四、問題的分析 對上證指數(shù)進行預測，需要對影響上證指數(shù)的主要因素進行分析進行分析1：對整體股票市場而言，其狀態(tài)最基本的表現(xiàn)方式是股票價格指數(shù)和成交量，而這兩項指標又受社會、政治、經濟、政策、心理等多種因素的影響。首先選擇表中可以查到的數(shù)據作為變量：MACD:DIFF, DEA;RSI;KDJ:D指標,J指標;WR;PSY;OBV 其次選擇以下變量：財政收入增長率、財政支出增長率、貨幣供應量、貨幣流通量、居民消費價格指數(shù)、固定資產投資情況。由于股民心理受收盤價和成交量的影響，故對上證指數(shù)的影響可用以下變量表示：今

5、日收盤價；今日成交量；昨日收盤價；昨日成交量；近5日平均收盤價；近5日平均成交量；近20日平均收盤價；近20日平均成交量. 以上均采用最近三個月的數(shù)據（包括上證指數(shù)）五、問題模型的建立和求解5.1問題的求解5.1.1多元線性回歸分析的數(shù)學模型2設明日收盤價為y,影響因素為22個，分別為，,它們之間有以下線性關系5.1.2模型求解使用SPSS3進行回歸分析得模型匯總模型RR 方調整 R 方標準 估計的誤差1.997a.994.9916.97007a. 預測變量: (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回歸332809.2261917516.275360.552.000b殘差2137.6024448.582總計334946.82863a. 因變量: yb. 預測變量: (常量), x22, x17, x15, x18, x10, x5, x16, x14, x19, x20, x13, x4, x12, x3, x9, x21, x2, x1, x11。系數(shù)a模型非標準化系數(shù)標準系數(shù)tSig.B標準 誤差試用版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. 因變量: y5.1.3 模型結果6、 結果分析與進一步推廣6.1多元線性回歸分析結果圖表從上圖可以看出標準化殘差的分布情況總體總體呈正態(tài)，集中在0的附近，這可以說明該回歸方程的準確性是比較高的。由以上圖表可知

9、較為精確與實際值接近。6.2預測模型準確情況分析在matlab中做出實際值與預測值的比較圖如下七、模型的評價優(yōu)點：1. 可推廣性。該多元線性回歸法可以應用到多變量線性關系問題評估中。2. 嚴謹性。SPSS與MATLAB相結合進行建模與模型評估，大大提高了模型的嚴謹性，較大程度的減少了人為計算可能會出現(xiàn)的誤差。4. 全面性。變量的選擇幾乎涵蓋了所有可能的影響因素，因此此建模過程是較為全面的。5. 實用性。本文所建模型與實際緊密聯(lián)系，結合實際情況對數(shù)據進行合理的處理，使模型更加貼近實際，通用性強，具有現(xiàn)實意義。缺點：1. 由于時間的限制，對數(shù)據的統(tǒng)計和整理還不完善，其中讀取數(shù)據量很大，有待進一步修

10、改。2. 由于選取變量的時間范圍較窄，因此模型的準確性還有待在數(shù)據更多的條件下進一步的驗證。八、參考文獻：1 鄒艷芬.上證指數(shù)的主要影響因素分析.江蘇 連云港：連云港化工高等?？茖W校學報，2002.2 李金海.多元回歸分析在預測中的應用.河北；河北工業(yè)大學學報，1996年第三期3 包鳳達等.多元回歸分析的軟件求解與案例解讀.數(shù)理統(tǒng)計與管理，2000年第五期附錄一：變量數(shù)據表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