時(shí)間序列作業(yè)VAR模型

一、案例分析的目的按國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、短期國庫券等構(gòu)成。我國參照國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)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MO;M2流動(dòng)性偏弱，但反映的是社會(huì)總需求的變化和未來通貨膨脹的壓力狀況，通常所說的貨幣供應(yīng)量，主要指 M2。M1反映著經(jīng)濟(jì)中的現(xiàn)實(shí)購買力； M2不僅反映現(xiàn)實(shí)的購買力，還反映潛在的購買力。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過高而M1過低，表明投資過熱、需求不旺，有危機(jī)風(fēng)險(xiǎn)；M1過高M(jìn)2過低，表明需求強(qiáng)勁、投資不足，有漲價(jià)風(fēng)險(xiǎn)。M1增加表示貨幣市場(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20.2萬億元，增長(zhǎng)29.5%，加快20.5個(gè)百分點(diǎn)。9月末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)的購買力與潛在購買力的相對(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年10月的月度數(shù)據(jù)，整理如下:時(shí)間M1M22002-0663144.00169601.202001-1156579.60154088.302002-0763487.80170851.102001-1259871.60158301.902002-0864868.80173250.902002-0160576.10159639.302002-0966797.00176982.402002-0258702.90160935.602002-1067100.30177294.202002-0359474.80164064.602002-1167992.80179736.302002-0460461.30164570.602002-1270882.10185007.302002-0561284.90166061.002003-0172405.70190488.302003-0269756.60190108.402003-0371438.80194487.302003-0471321.20196130.102003-0572777.80199505.202003-0675923.20204931.402003-0776152.80206193.102003-0877033.00210591.902003-0979163.90213567.102003-1080267.10214469.402003-1180814.90216351.702003-1284118.60221222.802004-0183805.90225101.902004-0283556.40227050.702004-0385815.60231654.602004-0485603.60233627.902004-0586780.40234842.402004-0688627.10238427.502004-0787982.20238127.002004-0889125.30239729.202004-0990439.10243756.902004-1090782.50243740.302004-1192387.10247135.602004-1295969.70254107.002005-0197079.00257708.502005-0292815.00259357.302005-0394743.20264588.902005-0494593.70266992.702005-0595802.00269240.502005-0698601.30275785.502005-0797674.10276966.302005-0899377.70281288.202005-09100964.00287438.302005-10101752.00287591.602005-11104125.80292350.402005-12107278.70298755.702006-01107250.70303571.702006-02104357.10304516.302006-03106737.10310490.702006-04106389.10313702.302006-05109219.20316709.802006-06112342.40322756.402006-07112653.00324010.802006-08114845.70327886.702006-09116814.10331865.402006-10118360.00332747.202006-11121645.00337504.202006-12126035.10345603.602007-01128484.10351498.802007-02126258.10358659.302007-03127881.30364093.702007-04127677.76367425.572007-05130275.80369718.152007-06135847.40377832.152007-07136237.43383884.882007-08140993.21387205.042007-09142591.57393098.912007-10144649.33394204.172007-11148009.82399757.912007-12152519.17403401.302008-01154872.59417846.172008-02150177.88421037.842008-03150867.47423054.532008-04151681.41429240.912008-05153344.75436221.602008-06154820.15443141.022008-07154992.44446362.172008-08156889.92448846.682008-09155748.97452898.712008-10157194.36453133.322008-11157826.63458644.662008-12166217.13475166.602009-01165214.34496135.312009-02166149.60506708.072009-03176541.13530626.712009-04178213.57540481.212009-05182025.58548263.512009-06193138.15568916.202009-07195889.27573102.852009-08200394.83576698.952009-09201708.14585405.342009-10207545.74586643.292009-11212493.18594604.722009-12220001.51606225.012010-01229588.98625609.292010-02224286.95636072.262010-03229397.93649947.462010-04233909.76656561.222010-05236497.88663351.372010-06240580.00673921.722010-07240664.07674051.482010-08244340.64687506.922010-09243821.90696471.502010-10253313.17699776.742010-11259420.32710339.032010-12266621.54725851.792011-01261765.01733884.832011-02259200.50736130.862011-03266255.48758130.882011-04266766.91757384.562011-05269289.63763409.222011-06274662.57780820.852011-07270545.66772923.652011-08273393.77780852.302011-09267193.16787406.202011-10276552.67816829.252011-11281416.37825493.942011-12289847.70851590.902012-01270010.40855898.892012-02270312.11867171.422012-03277998.11895565.502012-04274983.82889604.042012-05278656.31900048.772012-06287526.17924991.202012-07283090.68919072.402012-08285739.27924894.592012-09286788.21943688.752012-10293309.78936404.282012-11296883.05944832.352012-12308664.23974148.802013-01311228.55992129.252013-02296103.24998600.832013-03310898.291035858.372013-04307648.421032551.902013-05310204.481042169.162013-06313499.821054403.692013-07310596.461052212.342013-08314085.911061256.432013-09312330.341077379.162013-10319433.851070166.64數(shù)據(jù)來源：中經(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。01Q203(HC&W(17 03陽10M12T0DLW1SA——DLM2SA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)NullHypottiesis:DLM1_SAhasaunitrootEJtagenous:Constant.LinearTrendLagLength:3Automatic-IbasedonSIC.maxia^=13)i-StatisticProb?AugmentedDickev-Fullerteststatistic26004440.0269T^sterificalMlevel10%level-4.025426-3442474-3U6882士MacKinnon[1&96)one-sidedp-values.Augmented：Dickey-FuilerlestEquationDependent\ariaole:D〔DU/H_SA:Method:LeastSquaresDate:11/21/13^Tim&r22:13Sample(adjusted):2002M042013M1QIncludedobservations:139alteradjustmentsVariableCoefficientStd.Errort-StallSticPron.DLM1_8A{-1)-0.5698040154619-3.&604440.0033D(DLM1_SAC-1))-0537S560143011-3.761712o.ooaaLagLRFPELagLRFPEAICSCHQ0079.5241NA5296-09*13.39205-1333815*-1136421'10SO.346435610735.47e-0g-13.24850-13.21711-13.29S29268529499.711670633e-0g-13.36491-13.14533-13^7562389454&117.S11794.97e-09-13.44496-13.1376987351346365473e-09-13.49425^13.0991937824.588708484M9-1347142■1298857-13.275226910.537811.09574"4S9e-09*^1150439*■12.93374-13.272517911.90212,557885480e-O9「346538*12.80693-13.197028913.99093.4961745.036-091343498-12&837+-1313175991479091.3678475.29e-09-13.33612-12.55209-130472210918.39896059345533e-09-13.380141245332-130055611919.77362.2665915.56e*09-13.34006■12,33044-12.9258112924.39197.4739055.52e-09-13.34950-12.25209-12.90357Endogenousvariables:CLM1_3ADLM2_3AExogenousvariables:CDate:11/21/13Time22:16Sample:2001M112013M10Includedgasedations:131NullHypottiesis:DLM2_SAlasaunitrootExogenous:Constant.LinearTrend 「亙LagLength:0(Automatic-^basedonSIC.maxla^l3>t-StatisticProb.*AugmentedDickey-FuJle『te戲atistic出47344g.ooooTestcriticalvaluas:5%level10%level-4.023976-3.441777145474*MacKinnon(1990one-sidedp-values.Augmented'DIckey-FJlIerTestEquationDependent\ariaole:D〔DLh12_SA;Method:LeastSquaresDate:11/21/13-Time-22:13Sample(a^juste厲2002^012D1SM10Indudedobservations:142alteradjustments/ariaMe CoeffidentSta.ErrorL-StaLsticProh.DLM2_8A{-1) -0.97&421 00850GO -11.47844 0.0030C 0013456 0001641 3.202354O.OOtJO從而DLM1_SADLM2_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1indicateslagorderselectedbythecriterionLR:sequentialmodifiedLRteststatistic(eachtestat5%level)FPE:Finalpredictionerror■aIC:AkaikeinformationcriterionSC.SchwarzinformationcriterionLJC，LJrnnmnCiliimirbfriirnmfinmrritnriinrii從以上分析結(jié)果可以看出， FPEAICSCHC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)/&ctorAutoregressionEstimatesDate11/21H3Time:22:20Sample(adjusted).2002U062013M10Indudedobsenations:137afteradjustmentsStandarderrors(n()&t-statis1icsin[][3DLM1_SADLM2_SADLM1_SA(-1)-0.069634(0.10325)[-0.S6046]0.095411(0.06302)\1.49490]DUU1-SA(也-0.133202(0.104&S)[*132131^-0.035307(0.06463)(-1.31997]DLFJ1_SA(-J>0.399511(0.0390S)[4.02190]0.034087(0.06122)(05C55SJDUU1_SA(-4)0.189854[009911)[1,91550>-0.019012(0.06124)[-0.31044]DLM1_3A(-5)0013027-00546&4DLM1_3A(-5)0.018027[0.10149)10177&2}-00S46Q4(D.0e271)(-1.0301B]JL□LM1_SA(-5)-0.021651[0.09932)I-022Q01J-0.0351&4(0.OC137)[-057202JDLM2_SA(-1)0,252353￡0.17377)-0.066025(0.10737)[1,45222)[-0.61493]FlDL岐醐勺0463808(0.17259)[^71637]0.213929(0.106E4)I2.00S17]DLFJ2_SA(-J>-0.467222[0.17520)1-2.50973}0.092752(0.10825)JDS5580IDLM2_SA(-4)0J13M5[017S48)[0.54225)0.127118(0.10905)(1.165F4JDLM2_3A(-5)-0.222503-0112343￥

DLM2_3A(-4)□113345(0.17648)[064225]0127118(0.10905)11.16574]DLM2_SA(-5)-0.222503(0.17524)H，2697S{-0.112943(0,10329)[-104309]DLM2_SA(-5)D47S4S0[0.1733C)[2.75991J0.074901(Q.10712)10.65923]G-0.001105(0.0041C)(-026543^0.010102(0.00257)13.92567]R-square(i0.2711800115074心氏R-squared0200650{).029436Sumsq.resids00143990005497S.E.equation0.0107760.005558nFstatist!c3844845134^730Loglikelthood433.1041499.0626AkaJkeWC-5.132907-7.095804Schwarz8G-5855829-6.618725WeanGSependenf00119+a0013705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)。F?ootsofCharacteristicFoiynornialEndogenousvariates:DLM1_Sa.DLM2_SAExogenousvarianles:CLagspecification.16Date;11/21/13Time；2224RoctModulus0818982*013039210.8292970818982*0130392i0.829297-0.304490-077044410.S28431-0.304490+0.770444i0,3284310.001233-07034601D70B4510001233^070845010.7084610463439-044244310.6553390.4&3439+0.44244310.655339-C62740B-O144S09i0.643979-0.6274G6+0144909i0,643979-0.449137-0.395942!0599406■0449137^0396942i0599406NorootIlesoutsidetheunitcircle/.ARsatjstiesthestabilityconditian.tnverseRootsotARCharacteristicPolynomial1.0”一―TOC\o"1-5"\h\z?塞\ I0.5 **I ■? +0.0? 4-0.5 * | * /4k-i.Q —-r--'' F F F F 叫\(zhòng)o"CurrentDocument"-1.5-ta-a.5 ao c.5 to 1,5因此，VAR滿足平穩(wěn)性的條件。接下來進(jìn)行殘差的獨(dú)立性檢驗(yàn)血 澄dt蹙wtk2-StdLrr.冬汕匸?主WIXMgDLMtjSAHJ C^rDtWI^SA.'tXW.SAf-ri3-i-60 T￥[..7 r,，- }~J 0'E-r~3~~~~~3~'<1 r 1 1 1 r 1 1 1 1 1 1亠7-1 1 1 V 1 ■ 1 1 1 1 q一1 1CWlXMLSAXMT_5A：-I 倒4化*DL惦二黏門：；-j-z-'..n1 1-申c 7T? . 1飛。] j v 49… ！』-2-J=t3 3 1 4rI;ig11 <3k 1 1 I 1 1 ■ ? 1 1■I]i1f?I5MS1'n所以殘差不存在自相關(guān)性，滿足獨(dú)立性假設(shè)。、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)VAR模型確定的滯后階數(shù)，來確定滯后階數(shù)，本例的滯后階數(shù)為6.PainAiseGrangerCausaIit■/TestsDale:11/21/UTime:22:32Sample.2001M112013M10Lags：6NullHypothesis: ObsF-statisticFro*DLM2_SAdoesnotGrangerCajseDLFJ1_SA 137 +.23057 00007DLM1_SAdoesnotGrangerCauseDLM2_SA 1.25614 0.2S2&（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關(guān)。DisptcyCcmlir.edGrtphsdl(11.5bdlnZ'-EE*DisplaynfcrTrator.*KacpCTiECK■dlnlDisptcyCcmlir.edGrtphsdl(11.5bdlnZ'-EE*DisplaynfcrTrator.*KacpCTiECK■dlnlsa41niZ_36R-oponscStandard&rcrakraHum#Adialytic(iJs/rftpt?IMonteCarloRepctx11-iJ1COPtri36"I, — - -AccumiLateiKeiponsesgflf常rwegit時(shí)OtSD.in-watCFifiTZSE.也CE7*3UJ1_tABM2M2和M2的數(shù)量有觀察上圖，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)上的密切的關(guān)系，從時(shí)間長(zhǎng)短來看，M1對(duì)于M2的長(zhǎng)期影響要大于短期影響， 而且M1對(duì)于M2的短期影響要顯著些。（三）方差分解在VAR的輸入窗口中,VariarcsDecompositionofDLW1_SAPeriodSE. DLMlJSADLM2_SA1D.010776100.00000.0000000.010666983431U1.656840001113393844766.1552420,01163239.0522910.537710,01215686.5912613.10OT20.01216096.S392613.110740.01247284.9078515.09212e0.012525949136415.08635g00125490460101153SS9910001260084.2931115.70669110012621842856315.7143712D.01262384.2022715.71773130.01263184.1901715.SC9S3140012638841763115.3236915001263984177G715S22Q31&0012640&415298156370217001264284.1598915.84011ISD.01264284.1505515.83945190.01264394.11516115-83339200.012643&41508515.83915210012643341504215G3953莖2w-v1U*VU71727D21001264384150421503953220.0126448415171158382923001264484.151701563&3D240.01264494.1S12515.83375250.012644&4J614315.S3857260.012C4484.16-14915.83951270012644841512915.833712Q001264484161151582385290.01264484.1511715.63&83300.01264484.1611115S3S89310.012644841610215.82898320012C4484161021583B98330012644841610115S339934001264484.1509815.8390235001264434.1&09615.63902360.01264434.1^09915.63902■/'ariariceDecompositionofDLM2_SA:PariodSEDLM1.SADLM2_SA10.0066583D.70&Q269.2S49820.006714J1.559876S.44013a0.00665030.3^6816960319斗0.006&2931547416345259&Q00690431.694746330526

/arianceDecompositionorCLTui2_SA'PeriodSE.DLM