1、基于ARMA1型的社會融資規模增長分析ARM模型實驗第一部分 實驗分析目的及方法一般說來,若時間序列滿足平穩隨機過程的性質,則可用經典的ARMAI型進行建模和預則。但是,由于金融時間序列隨機波動較大，很少滿足ARMAI型的適用條件，無法直接采用該模型進行處理。通過對數化及差分處理后 , 將原本非平穩的序列處理為近似平穩的序列,可以采用ARM喂型進行建模和分析。第二部分 實驗數據2.1 數據來源數據來源于中經網統計數據庫。具體數據見附錄表5.1 。2.2 所選數據變量社會融資規模指一定時期內（每月、每季或每年）實體經濟從金融體系獲得的全部資金總額，為一增量概念，即期末余額減去期初余額的差額，或當

2、期發行或發生額扣除當期兌付或償還額的差額。社會融資規模作為重要的宏觀監測指標，由實體經濟需求所決定，反映金融體系對實體經濟的資金量支持。本實驗擬選取2005 年 11 月到 2014年 9 月我國以月為單位的社會融資規模的數據來構建ARM喂型，并利用該模型進行分析預測。第三部分ARMA真型構建3.1 判斷序列的平穩性首先繪制出 M 的折線圖，結果如下圖：圖3.1社會融資規模M曲線圖從圖中可以看出， 社會融資規模 M序列具有一定的趨勢性，由此可以初步判斷該序列是非平穩的。此外， m在每年同時期出現相同白變動趨勢，表明m還存在季節特征。下面對m的平穩性和季節性進行進一步檢驗。為了減少m的變動趨勢以

3、及異方差性，先對 m進行對數化處理，記為lm,其時序圖如下:LM105-1QQ- 95- 9。-S.5- &0- 7S- 7J- 邑5-20-0S2007 20OS 20口920102011201220112014對數化后的趨勢性減弱，但仍存在一定的趨勢性，1、面觀察lm的自相關圖表3.1lm的自相關圖Date: 11/02/14 T1me：2?:25Sample: 2005M11 2014M0SIncluded observations: 107AutocorrelationPartial CorrelationACPACQ-StatProb0 5290.52930,319110 0

4、000 574040967 45911121 HOUZJ1U 548101 091130 253U uuu1140.4470 015123.68ocoo11'60.410,071148.000.00D1二160.358-0.003162840.0001111JIJ1:178 g0 4220 3980.4010.1300.0950 101183 64202.09221.260.0000000000011:1100.43S0 109244.36000011110.373-o aia261 280 00011120 4970.192291.650.00011130 318'0.164

5、304 22000011140.330-0 090317.84000011150.267-0.142326.91o.coo11ie0.179-0 119331.0000001J1170.2540 071339 34ocoo111180 127西9341 440.00011190 1950.007346.02000n11200.1850.022350.6000011210.2300 144357.7600011,1:22230.2370 1770 029-0.027365.47309 840000.001J12403160.150383 39aoo1111:.Ji 口11111:1 111111

6、25262726293。0.1230.1110.094-0.0010 029-001B0.142-0 130-OOS9-0 059 HUB 口0 044336.04397 00399.09399 09389 22389.260.000000000000.000001 111111 " 1'匚11R "313233-0.0270.0010.0550.053-0.107-0 0130 1270.053339.37389.37389.0439Q.580000000000,00L00D上表口以乍1出，該lm序列的PACF只在滯舟-期、二期和三期是顯著的,ACF隨著滯后結束的

7、增加慢慢衰減至0,由此可以看出該序列表現出一定的平穩性。進一步進行單位根檢驗，由于存在較弱日勺趨勢性且均值小為零，選擇存衽趨勢壩日勺形式，開根據AIC目動選擇之后結束，單便根檢驗結果如下：表3.2單位根輸出結果Null Hypothesis: LM has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic - based on SIC, maxlag=12)Augmented Dickey-Fuller test statistic-8.6746460.0000Test critical values:1%

8、 level-4.0469255% level-3.45276410% level-3.151911t-StatisticProb.*MacKinnon (1996) one-sided p-values.單位根統計量 ADF=-8.674646小于臨界值，且 P為0.0000,因此該序列不存在單位根, 即該序列是平穩序列。由于趨勢性會掩蓋季節性，從lm圖中可以看出，該序列有一定的季節性，為了分析季節性，對lm進行差分處理，進一步觀察季節性:DLM圖3.3 dlm曲線圖觀察dlm的自相關表：表3.3 dlm的自相關圖Date: 11/02/14 Time: 22:35Sample: 2005M

9、11 2014M09Included observations: 106Autocorrelation Partial CorrelationAC PAC Q-Stat Prob*|.|*|.|1 -0.566 -0.56634.9340.000.|*20.113 -0.30536.3410.000.|.|*|.|30.032-0.09336.4550.000*|.|*|.|4-0.084-0.11437.2440.000.|*|.|.|50.1050.01538.4940.000*|.|*|.|6-0.182-0.18242.2960.000.|*|*|.|70.105-0.15643.56

10、30.000.|.|*|.|8-0.058-0.17143.9540.000.|.|*|.|9-0.019-0.19643.9960.000.|*|.|.|100.110-0.04545.4290.000*|.|*|.|11-0.242-0.32952.5010.000.|*|.1.1120.3630.02368.5160.000*|.|.1.113-0.2020.03273.5340.000.|*|.|*|140.1010.12574.8150.000.|.|.|*|150.0040.14174.8170.000*|.|*|.|16-0.161-0.08978.1100.000.|*|.1.

11、1170.2190.03784.2520.000*|.|.1.118-0.221-0.03690.6230.000.|*|.1.1190.089-0.04691.6620.000*|.|*|.|20-0.080-0.15892.5160.000.|.|.1.1210.067-0.03993.1150.000.|.|.1.1220.0680.05693.7490.000*|.|*|.|23-0.231-0.130101.080.000.|*|.|*|240.3590.116119.040.000*|.|.|*|25-0.1890.123124.090.000.|.|.1.1260.0320.03

12、4124.230.000.|.|.1.1270.0590.037124.740.000*|.|.1.128-0.1260.044127.080.000.|*|*|.|290.087-0.079128.210.000.|.|.|*|30-0.0500.092128.580.000.|.|.1.131-0.037-0.019128.790.000.|.|*|.|32-0.035-0.113128.970.000.|.|.1.1330.041-0.056129.240.000.|*|.1.1340.078-0.027130.210.000*|.|*|.|35-0.215-0.197137.640.0

13、00.|*|.|*|360.3800.130161.260.000由dlm的自相關圖可知，dlm在滯后期為12、24、36等差的自相關系數均顯著異于零。因此該序列為以12為周期呈現季節性，而且季節自相關系數并沒有衰減至零，因此為了考慮這種季節性，進行季節性差分，得新變量sdlm:觀察sdlm的自相關圖：表3.4 sdlm的自相關圖Date: 11/02/14 Time: 22:40Sample: 2005M11 2014M09Included observations: 94AutocorrelationPartial CorrelationACPACQ-StatProb*|.|*|.|1-0

14、.505-0.50524.7670.000.1.1*|.|2-0.057-0.41925.0820.000.1.1*|.|30.073-0.29225.6090.000.|*|.|.|40.1600.06728.1690.000*|.|.*|.|5-0.264-0.12535.2520.000.|*|.*|.|60.098-0.11036.2440.000.|*|.|.|70.0980.01937.2430.000.|.|.|*|8-0.0410.08237.4190.000.*|.|.|.|9-0.132-0.03839.2750.000.|*|.*|.|100.076-0.13939.90

15、20.000.|*|.|*|110.2270.24745.4850.000*|.|*|.|12-0.459-0.25968.6470.000.|*|*|.|130.193-0.25172.7770.000.|*|.*|.|140.132-0.10174.7530.000.*|.|.*|.|15-0.142-0.18977.0560.000.1.1.|.|16-0.053-0.05677.3780.000.|*|.|*|170.2330.09183.7510.000*|.|.*|.|18-0.234-0.17990.2580.000.|*|.|.|190.1020.05491.5050.000.

16、1.1.|.|20-0.052-0.03591.8410.000.|*|.|.|210.123-0.00993.7140.000.1.1.|*|22-0.0590.12094.1500.000.1.1.|*|23-0.0110.21594.1660.000.1.1.*|.|24-0.032-0.17094.3010.000.|*|.*|.|250.088-0.13795.3030.000.*|.|.|.|26-0.105-0.03496.7600.000.|*|.*|.|270.077-0.11697.5620.000.1.1.*|.|28-0.054-0.17897.9670.000.1.1

17、.|.|290.0100.03297.9820.000.|*|.|.|300.1020.03999.4570.000.*|.|.*|.|31-0.179-0.099104.060.000.1.1.|.|320.071-0.058104.790.000.1.1.*|.|330.031-0.066104.930.000.*|.|.*|.|34-0.089-0.144106.130.000.|.|.|*|350.0360.082106.320.000.|*|.*|.|360.105-0.102108.050.000Sdlm在滯后期24之后的季節 ACF和PACF已衰減至零，下面對 sdlm建立SAR

18、MA模型。3.2模型參數識別由表3.4 sdlm的自相關圖的自相關圖可知，偏自相關系數在3階后都落在兩倍標準差的范圍以內，即不顯著異于零。自相關系數在 1階和12階顯著異于零。因此 SARMA(p,q)模型中選擇p、q均不超過3。此外，由于高階移動平均模型估計較為困難而且自回歸模型可以表示無窮階的移動平均過程，因此Q盡可能取小。擬選擇SARMA(1,0)(1,0)12、SARMA(1,0)(1,(1) 12、SARMA(1,1) (1,0) 12、SARMA(1,1) (1,1) 12、SARMA(2,0) (1,0) 12、SARMA(2,0)(1,1) 12、SARMA(3,0) (1,0

19、) 12、SARMA(3,0) (1,1) 12 八個模型來擬合 sdlnm。3.3模型參數估計以SARMA(1,0) (1,0) 12模型為例，分析該模型的估計及殘差的檢驗，其他模型類似。回歸結果為：表3.5 SARMA(1,0) (1,0) 12模型估計結果Dependent Variable: SDLMMethod: Least SquaresDate: 11/02/14 Time: 22:50Sample (adjusted): 2008M01 2014M09Included observations: 81 after adjustmentsConvergence achieved

20、after 6 iterationsVariableCoefficientStd. Errort-StatisticProb.C-0.0053050.023352-0.2271650.8209AR(1)-0.4908550.098580-4.9792560.0000SAR(12)-0.5485090.096987-5.6554710.0000R-squared0.448053Mean dependent var-0.004983Adjusted R-squared0.433901S.D. dependent var0.644876S.E. of regression0.485202Akaike

21、 info criterion1.427829Sum squared resid18.36280Schwarz criterion1.516512Log likelihood-54.82707Hannan-Quinn criter.1.463410F-statistic31.65901Durbin-Watson stat2.348799Prob(F-statistic)0.000000Inverted AR Roots.92+.25i.92-.25i.67+.67i.67-.67i.25-.92i.25+.92i-.25-.92i-.25+.92i-.49-.67-.67i-.67-.67i-

22、.92+.25i由表3.3可知，AR與sar (12)的P值均小于0.05,參數顯著，可以通過檢驗。該模 型AIC為1.427829, SC值為1.516512回歸結果的最后一部分表示該模型滯后多項式的反特 征根，小于1,因此該模型是平穩的。卜面對殘差進行檢驗。觀察殘差的自相關圖:表3.6 SARMA(1,0) (1,0) 12模型的殘差檢驗結果Date: 11/02/14 Time:Sample： 200SM01 2Q14M09Included cbservations: 010-statistic probabilities a<usledfor2 ARI.1 Aternn(s)Au

23、to co rrelationPartial CorrelationACPAC(ystetProbd d 1-0.181-0.1S12.7560Iil= 2*0374-0420U65Di i匚i30.075-0.12215,1400.000 i 40.124-0.05616 4820000|Q IE 5-0.137-0.15918 1450.0001p &0014-Q.0&418.15?a.001 n >70,1630.0&121,2020.001 i i a*00300.03021 2B30.0D2匚 i g-0145-0.03523 2460.002 i i

24、100 0500.00723,4340.003 j i ii0.047-0.02523700C.005匚匚i12-0172-QJ8026,5830.003 口 i 130 0850.00027 2880.CD4 nii 1 i140.1550.03628 7150.003ir i 匚 i15-0150-0.09232 0070.002ii ) '16OQOG0.082012a.0041 J111170 0B30.020327320.005 D "l '18-0.094-0.07333.6 陰0.006i ig*0 055-0.01 B33 9930.0D8i | ii

25、匚 i200.015-0.13034 0160.053i i | 210 0Q1-0.021M95 口0.014 J 12200790.13635,即0017 1 Ji230 0330.18135,7"0023匚 i匚i24-0 258-0.21643 5430.0D4i 1 i 1 2500310.01843 7570.0D6i | ii匚 i260017-0.162437920.0081 1 I E '2T0 022-012143 8510.0111匚1C 128-Q.1Q2-Q.21?45,1650.Q111 n ji2g0JS4QJ9949,521QQU51 1 1i

26、 300030-0.05649 6360.CD7匚 1i C 31-0 256-0.1U584460.00111i I 320 004-0.04658 4470.001 n i H hnn 、4 ucn nnn GFb"由表3.6可知， 由Q統計量可知殘差存在自相關性，P值遠小于0.05,因此殘差不滿足白噪聲的假設。將八個模型的估計結果進行匯總如下:表3.7不同SARMA模型的特征匯總表AICSC平穩性可逆性殘差是否滿 足白噪聲SARMA(1,0) (1,0) 121.4278291.516512是是否SARMA(1,0) (1,1) 121.0954341.095434是是否SAR

27、MA(1,1) (1,0) 121.2061811.206181是是:是SARMA(1,1) (1,1) 120.8624961.010301是是P是SARMA(2,0) (1,0) 121.0103011.424354是是否SARMA(2,0) (1,1) 121.0002481.149124是是r否SARMA(3,0) (1,0) 121.2417641.391729是是r是SARMA(3,0) (1,1) 121.3917290.959325是是是綜合來看，根據信息準則，應選擇 SARMA(1,1) (1,1) 12對數據進行擬合是最優的。擬合結果 為：表3.8 SARMA(1,1) (

28、1,1) 12模型估計結果Dependent Variable: SDLMMethod: Least SquaresDate: 11/02/14 Time: 23:16Sample (adjusted): 2008M01 2014M09Included observations: 81 after adjustmentsConvergence achieved after 13 iterations MA Backcast: 2006M12 2007M12VariableCoefficientStd. Errort-StatisticProb.C-0.0068210.002943-2.3177

29、820.0232AR(1)0.0186630.1411680.1322030.8952SAR(12)-0.2016230.120638-1.6713130.0988MA(1)-0.8339470.080352-10.378650.0000SMA(12)-0.8603910.041002-20.984270.0000R-squared0.701510Mean dependent var-0.004983Adjusted R-squared0.685800S.D. dependent var0.644876S.E. of regression0.361475Akaike info criterio

30、n0.862496Sum squared resid9.930500Schwarz criterion1.010301Log likelihood-29.93107Hannan-Quinn criter.0.921797F-statistic44.65381Durbin-Watson stat2.003373Prob(F-statistic)0.000000Inverted AR Roots.85+.23i.85-.23i.62-.62i.62+.62i.23+.85i.23-.85i.02-.23-.85i-.23+.85i-.62+.62i-.62+.62i-.85-.23i-.85+.2

31、3iInverted MA Roots.99.86+.49i.86-.49i.83.49-.86i.49+.86i.00-.99i-.00+.99i-.49-.86i-.49+.86i-.86-.49i-.86+.49i-.9920M3.2模型預測在SARMA(1,1) (1,1) 12估計方程下選擇動態估計，預測2014年10月至12月的序列值，并將結果保存在sdlnmf中，預測情況如下：For&cast SDLMF Actual: SDLMForecasl sample: S014M05 S014M09Included observations: 5Root Mean Square

32、d Error 0.648539Mean Absolute Error 0.461327Mean Abs. Percent Error 62.91846Theil Inequality Goefficient 0.53&1 MBias Proporttori0.000107Variance Proportion 0.64 9319 Covariance Proportton 0350574SDLMF TiSE圖中左邊是預測值與置信區間，右邊是預測的誤差。Theil不等系數中bias proportion表示偏誤，即預測均值與真實均值的偏離程度，本例中 bias proportion的值

33、為0.000107,預 測均值與真實值偏離較小；variance proportion表示方差誤，用來反映預測波動與真實波動之間的差異，本例variance proportion為0.649319,則說明預測波動與真實波動的差異較大； covariance proportion表示協方差誤，反映殘存非系統性預測誤差，本例中該值為 0.350574, 該誤差占比越大，預測效果越好。本例中的協方差誤要小于方差誤，因此預測效果較差。附錄具體數據表5.1社會融資規模M指標社會融資規模地區全國頻度月單位億元2002-01-4722002-022892002-0331362002-0411512002-0

34、517742002-0626212002-078132002-0815852002-0935072002-107952002-1118052002-1231092003-0133862003-029982003-0340412003-0426222003-0529712003-0658422003-0713442003-0833212003-0940402003-1012182003-1118322003-1224982004-0121142004-024382004-0365572004-0427312004-0524432004-0632292004-075902004-081501200

35、4-0929812004-104832004-1119772004-1235862005-0136202005-028242005-0341892005-0419992005-0519682005-0647232005-076292005-0820972005-0960412005-10-9742005-1123682005-1225242006-0163232006-0217372006-0374722006-0433252006-0537852006-0638432006-0722542006-0833622006-0930772006-108942006-1127882006-12383

36、72007-0169082007-0230832007-0363112007-0461032007-0538242007-0670422007-0731002007-0869612007-0952902007-1036882007-1130732007-1242812008-01108592008-0247312008-0363912008-0470762008-0556782008-0659762008-0748902008-0845752008-0956592008-1012882008-1145172008-1281642009-01139902009-02111312009-03220

37、112009-0454522009-05149592009-06210672009-0773882009-0876502009-09118712009-1059852009-1195012009-1281002010-01205502010-02108772010-03138302010-04149192010-05108052010-06101962010-0772022010-08106462010-09112242010-1086082010-11105542010-12107802011-01175602011-0264682011-03182122011-04136732011-05

38、108542011-06108732011-0753932011-08107412011-0942792011-1079082011-1195812011-12127442012-0197542012-02104312012-03187042012-0496372012-05114322012-06178022012-07105222012-08124752012-09164622012-10129062012-11112252012-12162822013-01254462013-02107052013-03255032013-04176292013-05118712013-06103752013-0781912013-08158412013-09141202013-1086452013-11123102013-12125322014-0126003.942014-029369.772014-0320934.492014-0415259.452014-0514013.272014-0619673.172014-072736.942014-089576.522014-0910522.06存在問題本次應用ARMA模型分析數據的過程存在不少問題，在整個過程中感覺對模型的理解 還不夠深入，有一些細節沒有理解清楚，