時(shí)間序列作業(yè)VAR模型

1、精品- 可編輯 -一、案例分析的目的按國(guó)際貨幣基金組織的劃分口徑可以把貨幣供給劃分為：M0 （現(xiàn)鈔）：是指流通于銀行體系以外的現(xiàn)鈔，即居民手中的現(xiàn)鈔和企業(yè)單位的備用金，不 包括商業(yè)銀行的庫(kù)存現(xiàn)金。M1 （狹義貨幣）：M0加上商業(yè)銀行活期存款構(gòu)成。M2 （廣義貨幣）：由M1加上準(zhǔn)貨幣構(gòu)成。準(zhǔn)貨幣由銀行的定期存款、儲(chǔ)蓄存款、外幣存款 以及各種短期信用工具如銀行承兌匯票、短期國(guó)庫(kù)券等構(gòu)成。我國(guó)參照國(guó)際貨幣基金組織的劃分口徑，把貨幣供給層次劃分如下：M0 =現(xiàn)金M1 =M0 +活期存款M2 = M1+城鄉(xiāng)居民儲(chǔ)蓄存款+定期存款+其他存款M3=M2+商業(yè)票據(jù)+大額可轉(zhuǎn)讓定期存單在這三個(gè)層次中，M0的流動(dòng)

2、性最強(qiáng)，M1次之，M2的流動(dòng)性最差。M0與消費(fèi)變動(dòng)密 切相關(guān)，是最活躍的貨幣；M1反映居民和企業(yè)資金松緊變化， 是經(jīng)濟(jì)周期波動(dòng)的先行指標(biāo)， 流動(dòng)性僅次于M0；M2流動(dòng)性偏弱，但反映的是社會(huì)總需求的變化和未來(lái)通貨膨脹的壓力 狀況，通常所說(shuō)的貨幣供應(yīng)量，主要指M2。1. M1反映著經(jīng)濟(jì)中的現(xiàn)實(shí)購(gòu)買力；M2不僅反映現(xiàn)實(shí)的購(gòu)買力，還反映潛在的購(gòu)買力。若M1增速較快，則消費(fèi)和終端市場(chǎng)活躍；若M2增速較快，則投資和中間市場(chǎng)活躍。中央銀 行和各商業(yè)銀行可以據(jù)此判定貨幣政策。M2過(guò)高而M1過(guò)低，表明投資過(guò)熱、需求不旺， 有危機(jī)風(fēng)險(xiǎn)；M1過(guò)高M(jìn)2過(guò)低，表明需求強(qiáng)勁、投資不足，有漲價(jià)風(fēng)險(xiǎn)。2. M1增加表示貨幣市

3、場(chǎng)流通性增強(qiáng)，M2中包括了M1，因此，再排除M1變化因素后，M2的增減代表了儲(chǔ)蓄的增加，貨幣流通性降低。根據(jù)央行的數(shù)據(jù)，2009年9月份貨幣供應(yīng)，M2余額58.5萬(wàn)億，同比增長(zhǎng)29.3%，比上年末加快11.5個(gè)百分點(diǎn)。M1余額20.2萬(wàn)億元，增長(zhǎng)29.5%，加快20.5個(gè)百分點(diǎn)。9月精品-可編輯-末Ml與M2的同比與環(huán)比增速雙雙創(chuàng)出了新高。與此同時(shí)，Ml的同比增速已經(jīng)超越了M2的同比增速，這意味著整個(gè)經(jīng)濟(jì)領(lǐng)域的活躍度已被有效激活，儲(chǔ)蓄開始活期化。本案例主要研究M1的數(shù)量與M2的數(shù)量關(guān)系。希望得出現(xiàn)實(shí)的購(gòu)買力與潛在購(gòu)買力 的相對(duì)關(guān)系。二、實(shí)驗(yàn)數(shù)據(jù)本實(shí)驗(yàn)選取的數(shù)據(jù)是2001年11月到2013時(shí)間M

4、1M22001-1156579.60154088.302001-1259871.60158301.902002-0160576.10159639.302002-0258702.90160935.602002-0359474.80164064.602002-0460461.30164570.602002-0561284.90166061.002002-0663144.00169601.202002-0763487.80170851.102002-0864868.80173250.902002-0966797.00176982.402002-1067100.30177294.202002-1167

5、992.80179736.302002-1270882.10185007.302003-0172405.70190488.302003-0269756.60190108.402003-0371438.80194487.302003-0471321.20196130.102003-0572777.80199505.202003-0675923.20204931.402003-0776152.80206193.102003-0877033.00210591.902003-0979163.90213567.102003-1080267.10214469.40年10月的月度數(shù)據(jù)，整理如下:2003-1

6、180814.90216351.702003-1284118.60221222.802004-0183805.90225101.902004-0283556.40227050.702004-0385815.60231654.602004-0485603.60233627.902004-0586780.40234842.402004-0688627.10238427.502004-0787982.20238127.002004-0889125.30239729.202004-0990439.10243756.902004-1090782.50243740.302004-1192387.10247

7、135.602004-1295969.70254107.002005-0197079.00257708.502005-0292815.00259357.302005-0394743.20264588.902005-0494593.70266992.702005-0595802.00269240.502005-0698601.30275785.502005-0797674.10276966.302005-0899377.70281288.202005-09100964.00287438.302005-10101752.00287591.602005-11104125.80292350.40200

8、5-12107278.70298755.702006-01107250.70303571.702006-02104357.10304516.302006-03106737.10310490.702006-04106389.10313702.302006-05109219.20316709.802006-06112342.40322756.402006-07112653.00324010.802006-08114845.70327886.702006-09116814.10331865.40精品-可編輯-2006-10118360.00332747.202006-11121645.0033750

9、4.202006-12126035.10345603.602007-01128484.10351498.802007-02126258.10358659.302007-03127881.30364093.702007-04127677.76367425.572007-05130275.80369718.152007-06135847.40377832.152007-07136237.43383884.882007-08140993.21387205.042007-09142591.57393098.912007-10144649.33394204.172007-11148009.8239975

10、7.912007-12152519.17403401.302008-01154872.59417846.172008-02150177.88421037.842008-03150867.47423054.532008-04151681.41429240.912008-05153344.75436221.602008-06154820.15443141.022008-07154992.44446362.172008-08156889.92448846.682008-09155748.97452898.712008-10157194.36453133.322008-11157826.6345864

11、4.662008-12166217.13475166.602009-01165214.34496135.312009-02166149.60506708.072009-03176541.13530626.712009-04178213.57540481.212009-05182025.58548263.512009-06193138.15568916.202009-07195889.27573102.852009-08200394.83576698.952009-09201708.14585405.342009-10207545.74586643.292009-11212493.1859460

12、4.722009-12220001.51606225.012010-01229588.98625609.292010-02224286.95636072.262010-03229397.93649947.462010-04233909.76656561.222010-05236497.88663351.372010-06240580.00673921.722010-07240664.07674051.482010-08244340.64687506.922010-09243821.90696471.502010-10253313.17699776.742010-11259420.3271033

13、9.032010-12266621.54725851.792011-01261765.01733884.832011-02259200.50736130.862011-03266255.48758130.882011-04266766.91757384.562011-05269289.63763409.222011-06274662.57780820.852011-07270545.66772923.652011-08273393.77780852.302011-09267193.16787406.202011-10276552.67816829.252011-11281416.3782549

14、3.942011-12289847.70851590.902012-01270010.40855898.89精品-可編輯-2012-02270312.11867171.422012-03277998.11895565.502012-04274983.82889604.042012-05278656.31900048.772012-06287526.17924991.202012-07283090.68919072.402012-08285739.27924894.592012-09286788.21943688.752012-10293309.78936404.282012-11296883.

15、05944832.352012-12308664.23974148.802013-01311228.55992129.252013-02296103.24998600.832013-03310898.291035858.372013-04307648.421032551.902013-05310204.481042169.162013-06313499.821054403.692013-07310596.461052212.342013-08314085.911061256.432013-09312330.341077379.162013-10319433.851070166.64數(shù)據(jù)來(lái)源：中

16、經(jīng)網(wǎng) 三、VAR模型的構(gòu)建（一）數(shù)據(jù)平穩(wěn)性檢驗(yàn)由于我的數(shù)據(jù)具有稍強(qiáng)的季節(jié)性，所以在剛開始的數(shù)據(jù)中做了消除季節(jié)性操作，趨勢(shì)性也較強(qiáng)，而且數(shù)據(jù)的單位根檢驗(yàn)接近1，所以先做一階差分，在其滿足平穩(wěn)性之后開始做VAR。Q1陀Q3 Q405-W (I?曲 昨101112UDLM1 SA DLM2 SA,根據(jù)圖形特征選取同時(shí)存在趨勢(shì)項(xiàng)和截距項(xiàng)進(jìn)行單位根檢驗(yàn)精品-可編輯-t-Giatisti cProb/usmented Dick&y-Fuiierte st statistic6304440.0269Test criticai values:1%lavel5 level1D% level-4 0254

17、26-3.442474-3.145882Null H.pothesis DLniSA has a unit rootExogenous: Constant. Linear TrendLag Length: 3 (Automatic-based on SIC, maxfag=13MacKinnon |J 996) ane-sidedp-valuesAugmented DicK&y*FuNer Test EquationD e pendent Variable: D(DLM 1_:Method: LeastDate： 11/21J15 Time: 22:12Sample (a(Jjuste

18、d): 2002M04 2013W10Included oser.ations 139 afler adjustmentsVariableCoefficientStd. Errort-StatlstlcPronDLM1_8A(-1)-0 5698040 154819-36S0W40 0003UCDLM1_SA-1)4. 5379660.143011-3.70V12Q.0003.lt-StatisticProbAuqmented Dick&j-Futierteststatistic-11.47&440.0000Test critical values;1 level幽level1

19、0% level-4.023975-3.4+1777-3.1+5474fMacKinnan (1936ane-sided p-values.Null H.pothesis DLl.12_SA has a unit rootExogenous: Constant. Linear TrendLag Length: 0 (Aulomatic-Based an SIC. majdag=13Augmented Dickey-Full er Test Equatio nDepcnaent VartaDJc: DDLM2_SA.;Method: Least SquawsDate： 11/21J15 Time

20、: 22:12SsmplB (adjusted)： 20Q2MD1 2013M10Included ot)sedations 142 afleradjusUnenTs/aria DieCoefficlenL Sta Error t-Statlstlc Prob.DLM2_SAi-1)G-0 976421 0.C85065 -11 4?344 0 0000C.Q13455 0.001641 6 2023G4 Q 0000從而DLM1_SA DLM2_SA在20%的顯著性水平上是平穩(wěn)序列。（二）VAR模型滯后階數(shù)的選擇精品-可編輯-精品-可編輯-嘗尸I %L-QIy viMC!7U石IPraEnd

21、ogenous variables DLM1_SADLM2_SA. Exogenous variables: CDate: 11/21/13 Time:22:16Sample: 2001M11 2013M10Included obseriafcons: 131LagLogLLRFPEAICSCHQC878 5241NA5.296-09-13.18206-1X33815*1136421*1B80.34C43.5610735.476-09-13.34SS013.21711-13 295292685 394997116705.38e09-13.36481U14533-13 275623E94.645

22、117.511794 97e-C9-13 44496-13.13768-13 320104SQ1J73513.453554.73e-?9-13J9425-13.09919-13,333725S04J7C24.58B70S4.B4H9S-114714212.99537811.09674*4.69eG9*13.50439-1293274-13.272511911.93219.5576364.696-09-114653S-129069S-13 1S762913.99093.490174503e-09-13 4349B-12.68874-13 131753914.79C

23、91 3678475 29e-09-13.38612-12.55209-11047221091S39S96 059345533609-13.36014 1245832-110055611919 77352.2656915.56e 09-13.34006-12330M-12 9298112924.39197.4738065.52e-C9-13.34950-1Z25209-12 503574indicates lag order selected b：r th& crTt&rionLR_sequential rnodified LRtest statistic電包c(diǎn)h test a

24、t &% lever； FPE: Final prediction error.AIC. .Mcaike information critertonSC: Schwarz informbom cnterianUO Urrsnrn Zi linn i nfn r im -n+i n nn卜c ri nn從以上分析結(jié)果可以看出，F(xiàn)PE AIC SC HQ都得出滯后階數(shù)為6時(shí)VAR模型是最優(yōu)的。因此選取的最優(yōu)滯后階數(shù)為6即K=6。（三）VAR模型的估計(jì)精品-可編輯-Vector Autoregression EstimatesDate: 11/21H3 Time:22:2CSample (a

25、djusted): 2002MQS 2013M10 included ooservatiors. 137after adjustments Standard errcrs :n f A t-statisties in )jLDLMISADLM2_SADLM1_SA(-1)00888S40.103291-0.5604910.095411CO. 063 82)1494901DLM1_SA(-2)-0.138202(0.10459)-1.32131-0.035307 (006483) -131997DLMl_SA(-3)0399511(0Q9909)4 021900 034697(006123)J0

26、.56656IDLM1_SA(-4)0.189854(0.09911)11.91550)-0D19012(006124)-0.310441DLM1_SA-5)00160274).064604DLM1_SA()0016027(0.10149)0.17762-0.064604(006271)-1.030181ADLM1_SA(-6)-0.021851(0.09932)-022Q01-0.035104(006137)-0.57202DLM2_SA(-1)0.252353(0.117377)1,45222,-0.066025(0.10737)(-061493DLhlE.SA卜2)04683090.17

27、2592.71 &370213829(0.106S4)200517DLM2_SA(-3)-0457222(0.17520)-260 9730.092752(010825)0 85680精品-可編輯-DLM2_SA(-4)0.113345(0.175480.54.225J012711B(0.10905)1 16574JDLM2_SA-5)-0 222503-0 112943精品-可編輯-0.113345(0 17648J(0 642250.127118(0.10905)1 165741JuDLM2_SA(-5)022250$0.17524)-1 26975-0,112943(0.1082

28、8)t-1.04309DLM2_SA(-6)0.478459(0.17336)(2.75991)0.074901 (010712) 0699231C-0.001105(0 00416)F0.265430.010102(00025?)3 925671R-squared0.2711S00,115074Adj R-squared0.2006500 029436Sumsqresi社s0.0143990 005497S.E. equaton0.0107760JO655Sr.statistic3.8448451343730Log likelihood433.1041499.0656Akaike AJC-6

29、 132907-7.095504Schwarz SC-5 B55829-6.818725Mean dependentQ.0119480 013705從上圖可以看出VAR模型的參數(shù)估計(jì)大多顯著（四）VAR模型的檢驗(yàn)VAR模型的檢驗(yàn)包括VAR模型的平穩(wěn)性檢測(cè)，以及殘差的獨(dú)立性檢驗(yàn)。精品-可編輯-Roots of CtiacacteristicPolynomialEndogenous variables: DLM1_SADLM2_SA Exogenous variables: CLag speciflcatioii: 1 6Date: 11p21/13 Tim: 22:24RootModulus0.

30、018982 -D.130392i0 8292970.818&82 4-0.13039210 829297-0.304490 - 0.77044410 828431-0.304490 0.77044410 8284310 00123S - 0.70S460i0.7084610.0Q1238 *0.70345010.7084610.483439 -0.442443i0 6553390.463439 * 0.44244310.655339-0.627486 - 0 144809(0 6429794),627406 + 0,144809!0.643979-0.449137 - 0.39594

31、2J0.59940&-0 449137+ 0 3G6942I0 599406fJa root lies outside the unit cirdG.VAR satistssthe stability condilion.Inverse Roots of AR Charactenstic Polynomial!1.00.5 0.0 * +-0 5* t-*-10-1 $-1I-0.5 do o5 tot5因此，VAR滿足平穩(wěn)性的條件。接下來(lái)進(jìn)行殘差的獨(dú)立性檢驗(yàn)精品-可編輯-所以殘差不存在自相關(guān)性，滿足獨(dú)立性假設(shè)。二、VAR模型的應(yīng)用（一）格蘭杰因果檢驗(yàn) 將兩個(gè)變量建立group，根據(jù)V

32、AR模型確定的滯后階數(shù)，來(lái)確定滯后階數(shù)，本例的滯后階 數(shù)為6.Pairwise Granger Causaib Tests Date: 11A21/13 Time: 22:32 Szmplm 2001F.I11 2C13L110 Lags: 6Null Hypothesis:ObsF-StatisticFeb,DLM2_SAdoes not Granger Gause DLM1_SA1374.200570.0007DLL11_SA does not Granger Cause DLM2_SA1 255140.2926（二）脈沖響應(yīng) 脈沖響應(yīng)函數(shù)受到變量順序的影響，因此，其結(jié)果的分析與主觀因素有

33、關(guān)。3 門訓(xùn)訕歹XM-1_SAi；-J：|SFXMi詁.戈切蟲罰：晞精品-可編輯-觀察上圖，M1和M2是相互影響的正向相關(guān)關(guān)系，這驗(yàn)證了市場(chǎng)上的M2和M2密切的關(guān)系，從時(shí)間長(zhǎng)短來(lái)看，M1對(duì)于M2的長(zhǎng)期影響要大于短期影響，而且M2的短期影響要顯著些。（三）方差分解在VAR的輸入窗口中,- Dftptay FormatTbl0 M tl ti pl e G峠hUcmtiried Graphs Rjespnse StendardErrcrs.rEHC-TIC0 Axalyti c (asjnnptatMnt4 CorlsrDISptalV IrHRaOHttnrinZmulsts：lespci ik

34、ies：dlnl_sa 41n2_saPeriods 36的數(shù)量有M1對(duì)于gflftpcw t5*義y E SD. hnDVit0i& ?2SKcma o* DwMfc, nRAUKMI苗DLMKCADLtJtA精品-可編輯-4Variance Decompasition of DLM1_SA:I IPeriodS.E.DLM1_SADLM2_SA10.010776100.00000.00000020.010966&e 343161.604O30.01113393.344766 15524240.01133289.0622S10.9377150.01215696 3912813

35、 1067260.0121SOS6 8892613.1107470 01247284.9Q738150521260012525S4.913&415.0863690.01254934.6010115.39699100.01260084.2931115.70689110.01252184.285631571437120.012623S4.2S22715.71773130.012631&4.1901715.S09S3140.01263834.1763115.82369150 01263934.17707IS.82293160.01264034.162981583702170.0125

36、4284.159891584011180.01264284160651583045190.012643&4 161611583839200.012643a4.ieo351583915210.012543&4.1504215.83958V&-V210.012543U* , VWJ3416042227P 21583958Ju220.012544B4.1S17115.83829230.01264494 1&1701583830240.012644&4.1&12515S3875250.01264484151431583657260.01204484151

37、4915.83851270.01264484.1&12915.83871280.01264484,1511515.S3SB5290.01264494.1611715.838B3300.01264434.1011115.83SS9310.01264434.161021583696320.01264484161021583898330012644&4.1610115.83895340 01264404.160981583902350.01264494.160981583902380.012644S41S09H1503902Yariance Decomposition of DLM2_8A:PeriodSE.DLM1.SADLM2.SA10.00655030 70502592949870.00671431 55987&8 440133000665030.3963169 6031940.00692931 5474158.4525950.00696431.594745830526精品-可編輯-van an匚EDecornposition of DLL12_3A:Period SEDLMVSA23456g1011123 456789012111111222456789I 1 1 1 4 12021222324石2627282930313233343536