張思成計(jì)量實(shí)驗(yàn)

張思成書(shū)上的金融計(jì)量學(xué)作業(yè)題一：獲得2001年之后中國(guó)月度CPI通貨膨脹率，用AR模型預(yù)測(cè)2011年9月及之后的點(diǎn)估計(jì)值和區(qū)間預(yù)測(cè)結(jié)果(樣本取2001年1月至2011年8月)Step1:從中國(guó)統(tǒng)計(jì)局網(wǎng)站找出2001年1月至2011年8月的居民消費(fèi)價(jià)格指數(shù)(上年同月=100)，在EViews中構(gòu)建序列cpi，dcpi=(cpi-100)%.Step2:作出dcpi序列的圖像，大致看出其符合平穩(wěn)序列的特征(如圖1)Step3:對(duì)序列dcpi進(jìn)行自相關(guān)性檢驗(yàn)，其中AC表現(xiàn)出拖尾現(xiàn)象，而PAC呈現(xiàn)一階截尾(如圖2)，考慮使用AR(1)模型進(jìn)行OLS回歸.□ate11/0 3Timer2112Wripl比2C01M012011M08Includedabservatians:128AutocorrelananPartialCorrelationACPACQ-StarProb10.93d10.93d114.370.0002D.B59-0.106211.90ODDO30700人0.073292050.000409&0.0823S7.60000060603-0100406.93000050.510-0.0644424?00007041400754SG020oco8o:m-010Aa/qss0DOD902Q5-Q135435540OQO100103-00314970300001100130QOJQ077-0.09243Z920OOQStep4:程序窗口輸入Isdcpicdcpi(-1),查看AR(1)模型的回歸情況DependentVariable:DCPIMethod:LeastSquaresDate:11/04/13lime:22:17Sample(adjusted):2001M022011M08Ineludedobservations:127afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C0.1067330.0831341.2838660.2016DCPI(-1)0.9713210.02420440.130170R-squared0.927972Meandependentvar2.388189AdjustedR-squared0.927396S.D.dependentvar2.536859S.E.ofregression0.683562Akaikeinfocriterion2.092624Sumsquaredresid58.40713Schwarzcriterion2.137414Loglikelihood-130.8816F-statistic1610.431Durbin-Watsonstat1.673332Prob(F-statistic)0從上表能夠看出R-squared很接近1,dcpi的t統(tǒng)計(jì)量很顯著，AIC和SIC都不大，于是可以決定用AR(1)進(jìn)行預(yù)測(cè)。Step5:以2001年1月至2011年8月的數(shù)據(jù)作為樣本，預(yù)測(cè)2011年9月至2012年7月的dcpi數(shù)值。可得出圖3。圖3于是做出了2011年9月至2012年8月的dcpi預(yù)測(cè)圖題二：以2001年1月至2011年8月的股票收益率為樣本，利用AR模型對(duì)2011年9月以及以后的股票收益率進(jìn)行預(yù)測(cè)，并比較不同模型結(jié)果的準(zhǔn)確度。Step1:首先在wind資訊上查到了2001年1月至2012年11月的以月度為頻率的股票指數(shù)，生成序列index。以該序列為基礎(chǔ)，生成股票收益率的序列i，公式為seriesi=((index-index(-1))/index(-1))*100 。并畫(huà)出收益率的graph011口1□011)1□1□11II匚111||1111||11111:11It1DateM'D礦13Tme1502Sample2001M012012M11includedAulocn吟isiionP制詡Corr&hlicn11ODateM'D礦13Tme1502Sample2001M012012M11includedAulocn吟isiionP制詡Corr&hlicn11O ACFACQ-StalProb110.097009713G990.2422Q212丁曲叩001930.091D0B19.25320.D26402660224197520QQ160.082Q02420JS20.D016與.067<173210370270124?OT723.57DDDD1e0.0014H223.5700.003900334010237970DD5110-0.031D0K23.S4&0.00B-0029WQ245740D12-009屯1時(shí)25271D.D14Step2:按題意用AR模型進(jìn)行預(yù)測(cè)，其中樣本為2001年1月至2011年8月，之后的數(shù)據(jù)作為對(duì)比，看預(yù)測(cè)值與實(shí)際值得差距。Step3:先用AR(2)進(jìn)行預(yù)測(cè)。輸入^ci(-1)i(-2) 看擬合程度DependentVariable.IMethod.LeastSquaresDate:11/06/13Time：15.09Sampleiadjusted)2001M042011M08Includedobser/ations12bafteradjustmentsVariableCoe幣匚imntStdErrort-StatisticProbC0.33945707513570451793065221(-1)00353520088131096792203350l(-2)02177330.088056247262100148R-squared0.058723Meandependentvar0524251AdjustedR-squared0.043292S.D.dependentvar6.54B112SE.ofregression0.361034Akaikeinfocriterion7.108749Sumsquaredresid8528.640Schwarzcriterion7176628Loglikelihood74129^F-statistic3805544Durbin-WatSQHstat2.017276Probfl；F-statistic；0024933擬合度并不好，但先用其生成預(yù)測(cè)序列if1.Step3:用AR(3)進(jìn)行預(yù)測(cè)，類似Step2的步驟，得到if2.同理獲取AR⑷，AR(5)的預(yù)測(cè)序列if3,if4.其擬合度都不高。將四個(gè)預(yù)測(cè)序列和實(shí)際序列放在同一張圖上看出用AR(5)預(yù)測(cè)的值較其他更接近實(shí)際值。下面是分別用ar(3)ar(4)ar(5)擬合的結(jié)果。

DependentVariable'IMethodLeastSquaresDate:11/06/13Time1521Sample(adjusted):2D01M052011M08DependentVariable'IMethodLeastSquaresDate:11/06/13Time1521Sample(adjusted):2D01M052011M08Includedobservations'124afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C031680907607600416437067781(-1)007503200913430.62143204130l(-2)0.2145170089108240522100177lf-3)0045228009090304&7535061&7R-squared0.060675Meandependentvar0.526032AdjustedR-sqjared0.037191S.D.dependentvar8.582767SEofregression8421652Akaikeinfocriterion7Sumsquaredresid8610.907Schwarzcriterion7S223&2Loglikelihood430.1354F-statistic2583752Durbin-V'.'atsonstat2016721ProbiF-statistic)00664S3這里i(-1)和i(-3)的系數(shù)幾乎為0,而且t統(tǒng)計(jì)量不顯著ar(3)的結(jié)果MethodLeastSquaresDate11/06/13Tme.1S23Sample(adjusted}:2001MOS2011M08Includedobsen/ations:123afteradjustmentsVariableCoetficieritStdErrort-StatisticProbC0.192610075144302563190.7962K-1)00655130069816072939304672K-3)01641B1006999613243200.C706K-3}0.0318410.0897270.3548670.72331(4}02233630.0895612.4939720ouoR-squared0.106927Meandependentvar0493832AdjustedR-squared0076654S..D.dspendentvar6610347S.E.ofregression8.273761Akaikeinfocriterion7103857Sumsquaredresid8077705Schwarzcriterion7218173Loglikelihood4318072F-statistic3532021Durbin-Watsonstat2.018586Prob(F-statistic)0009251ar(4)的結(jié)果MethOdLLeast[|SquareDate11/06/13Tim:15:25Sample(adjusted)2001MOT2011MOGIncludedobservations:122afteradjustmentsC01699520.76081002233840.8236IM)0.0547520.092878C01699520.76081002233840.8236IM)0.0547520.0928780.5335090.5567H-2J0.1629750.0906961.7969490.0749H-3J00235210.0919520.2557990.7986I河02210070.0906112.439062001621(-5}0.0471910.0925760.5097570.6112t-Statisti匚ProbR-squaned 01Q394SAdjust&dR-squared 0070538SEofregression B335301Sumsquaredresid 8059359Loglikelihood |4287352Du市"Watsonstat 1944806M&andependent*a「SDdependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)049648485458031126806"26470928365S50013728ar(5)的結(jié)果5.12-5.IJI I2011M10’2012MO112012M041112012M07IN2^12M10|A A3 A1 A4 A2相對(duì)于ar(2)ar(3)ar(4) ,ar⑸的預(yù)測(cè)稍微準(zhǔn)確，相信將階數(shù)增加到很大的時(shí)候可以比較接近真實(shí)值。題三：用ADF單位根檢驗(yàn)法檢驗(yàn)1978至2000年的GDP序列，并用ARIMA莫型預(yù)測(cè)2001年和2002年的GDPStepl:在中經(jīng)網(wǎng)數(shù)據(jù)庫(kù)找出1978至2002年的gdp數(shù)據(jù)，其中1978年至2000年的數(shù)據(jù)作為樣本，作出graph以及自相關(guān)圖Sample19782002Includedobservations:25AutocorrelationPartialCorrelationACPACQ-StatProbII□1□107110.71114.2080.000I=111205070003217400ODOI□l11130347-0.02S25.4360.0001Zl11140232-001027.17100001□111150177004523.22900001□1111601690.050291250.0001口11117014S002229舛700001■111190136001030.681000011111901180.00031266000011<1111000900.014316310.0001111110.057-0.02231.7860.0011I120020-00313180600011111可以看出gdp序列可能是非平穩(wěn)的。Step2:對(duì)該序列進(jìn)行ADF單位根檢驗(yàn)，以確定gdp序列的平穩(wěn)性。假設(shè)是情況3,即既帶有t趨勢(shì)項(xiàng)又帶有截距項(xiàng)。在選項(xiàng)中選擇Trendandintercept?？傻茫篘ullHypothesis:GDPhasaunitrootExogenousConstantLinearTrendLagLength2(AutomaticbasedonSIC.PAAXL7\G=5)t-SlatisticProb/AugmentedDickey-Fullerteststatistic-0.83009909463Testcriticalvalues'1%level5%level■444073910%level-36329%-3.254671*MacKinnon(1996)one-sidedp-valuesAugmentedDickey-FullerTestEquationDependentVariableD(GDP)MethodLeastSquaresDate：11/06/13Time:16:37SamplE(adjusted):19812002 T統(tǒng)計(jì)量的值遠(yuǎn)大于檢驗(yàn)水平1%5%10%勺的臨界值。因此拒絕原假設(shè)，即可認(rèn)為序列g(shù)dp是非平穩(wěn)的。Sample(adjusted):19812002Includedobservations22afteradjustmentsVariable CoefficientStdErrort-StatisticProbGDP(-1)■00207210.024962-0.8300990.4180D(GDP(-1))1.1937320.173350688626100000D(GDP(-2)>-06475730.177206-3.65434200020C-1531.4631027.351■14906910.1544@TREND(1978)34560081416963243902500260R-squared0921700Meandependent汨「5263.049AdjustedR-squared0903276SDdependentvar4294496SEofregression1335.606Ak自ikminfocriterion17.42987Sumsquaredresid30325324Schwarzcrirterion17.67684L口glikelihood-1867176F-statistic50.02841Durbin-Watsonstat2033307Prob(F-statistic)0000000其中g(shù)dp一階差分，gdp二階差分的系數(shù)，以及trend的系數(shù)都比較顯著，拒絕均為0的原假設(shè)。即可認(rèn)為該序列屬于第三種情況（既含趨勢(shì)項(xiàng)又含截距項(xiàng)）Step3:下面確定單位根的個(gè)數(shù)，由于gdp的一階滯后項(xiàng)和二階滯后項(xiàng)都有系數(shù)。直接用二階差分的ADF單位根來(lái)檢驗(yàn)。得出；■1i1■1i1i匚■ii1匚1□1]11=1匚1i匚11|■i11匚1i[1 ..1 ■一一」104660466667310.0172-0.3975.91J30.062J-0.2090.0567.16S60.0674-0410-0511122540.01654160054S13072002360070-0.91713.2370.0397-0.03i7.2B813.2780.0661階，4階處超出置信區(qū)間，PACF在t-StatisticProb.*AugmentedDickey-Fullerteststatistic叨974159 00288Testcriticalvalues. 1%level5%level10%level4532598-1673616-3277364'MacKinnon(1996)one-sidedp'ValuesWarningProbabilitiesandcriticalvaluescalculatedfor20observationsandmaynotbeaccurateforasamplesizeof19AugmentedDickey-FullerTestEquationDependentVariable:D(GDP3)Method.LeastSquaresDate:11/05/13Time.17:12Sample(adjusted):19842002Includedobservations.19afteradjustmentsVariableCoefficientStdErrort-StatisticProbD(GDP(-1).2)-1.5032280378251-3.97415900016D(GDP(-1).3)09486500299581316658500074D(GDP(-2).3)04484220.2811261.5950890.1347D(GDP(-3).3)07059680.3207932.2006980.0464C92109881081054085203804096@TREND(1978]-17.609806691794-0.2631550.7966R-squared0589312Meandependentvar1546842AdjustedR-squ白佗cf0.431355S.D.dependentvar2071.037SEofregression1561740Akaikeinfiocriterion17.79706Sumsquaredresid31707402Schwarzcriterion1809532Loglikelihood-1610722Fstatistic3.730834Du市in-Watsonstat1932590Prob(F'Statistic}0025815T統(tǒng)計(jì)量大于5%的臨界值，因此可以接受原假設(shè)。并且trend項(xiàng)的系數(shù)不顯著，可以認(rèn)為gdp的二階差分是平穩(wěn)的，即gdp序列是二階單整序列Step4:用ARIMA(p,d,q)模型來(lái)估計(jì)該序列，目前可以確定d=2。對(duì)gdp的二階差分進(jìn)行自相關(guān)圖分析Date:11/06/13Time1942Sample:19782002Includedobservations:23ACPACQ-StatPrabAutncorralationPartialCorrelationACPACQ-StatPrab1、2、4、5、6、7都超出。MA應(yīng)該是低階的，AR取2(滯后2階后變的很小)考慮用ARM(2,1)和ARM(2,2)來(lái)擬合經(jīng)過(guò)2階差分的GDP序列代碼為d(log(gdp),1,2)car⑵ar(1)ma(l)其中ARIMA(2,2,1)的結(jié)果為：DependentVariableD(LOG(GOP}12)MethodLeastSquaresDate.11/06/13Time.20.27Sample(adjuslAd)-19B32D00Includobservahons18afteradjustmentsConvergenceachievedafter145iterationsBackca5t.OFF(RootsofMAprocesstoolarge}VariablyCoeflicieritStdError t-StatisticProbC0.0226S200171B9 1.3104290.2095AR(2}-0.29148&0.271GS6 A1.0360680.3177ARID0.1610&20249B09 05447010529&MA(1}20080730614071 327010700056R-squared0.8601S6Meandependentvar0.0002&8AdjustedR-squared08301&9SD.dspendsntg0.093743SEofnegression0038630Akaikeinfocntenon-3476461Sumsquareresid0.Q20892Schwarzcriterion-3.278601Luglikelihood35.28815F-Statislic28.70382Durtiin-V'/atsDnistat1.327320PrDb(F-statistic)0J00DD3insertedARRooksInsertedMARootsQS+52i-201OS-52tEstimatefdApiocEssimnani