實(shí)驗(yàn)四-金融數(shù)據(jù)平穩(wěn)性檢驗(yàn)

實(shí)驗(yàn)四金融數(shù)據(jù)的平穩(wěn)性檢驗(yàn)實(shí)驗(yàn)?zāi)康睦斫饨?jīng)濟(jì)時(shí)間序列存在的不平穩(wěn)性，掌握ADF檢驗(yàn)平穩(wěn)性的方法。不平穩(wěn)的序列容易導(dǎo)致偽回歸問(wèn)題，掌握為解決偽回歸問(wèn)題引出的協(xié)整檢驗(yàn)，協(xié)整的概念和具體的協(xié)整檢驗(yàn)過(guò)程。協(xié)整描述了變量之間的長(zhǎng)期關(guān)系，為了進(jìn)一步研究變量之間的短期均衡是否存在，掌握誤差糾正模型方法。理解變量之間的因果關(guān)系的計(jì)量意義，掌握格蘭杰因果檢驗(yàn)方法?；靖拍钊绻粋€(gè)隨機(jī)過(guò)程的均值和方差在時(shí)間過(guò)程上都是常數(shù)，并且在任何兩時(shí)期的協(xié)方差值僅依賴于該兩時(shí)期間的距離或滯后，而不依賴于計(jì)算這個(gè)協(xié)方差的實(shí)際時(shí)間，就稱它為平穩(wěn)的。強(qiáng)調(diào)平穩(wěn)性是因?yàn)閷⒁粋€(gè)隨機(jī)游走變量〔即非平穩(wěn)數(shù)據(jù)〕對(duì)另一個(gè)隨機(jī)游走變量進(jìn)行回歸可能導(dǎo)致荒唐的結(jié)果，傳統(tǒng)的顯著性檢驗(yàn)將告知我們變量之間的關(guān)系是不存在的。這種情況就稱為“偽回歸”。實(shí)驗(yàn)內(nèi)容用Eviews來(lái)分析A股2014年4月10日至2018年5月15日深證成指股票與上證指數(shù)的兩只股票綜合指數(shù)1000個(gè)交易日收盤價(jià)數(shù)據(jù)，對(duì)數(shù)據(jù)進(jìn)行平穩(wěn)性檢驗(yàn)。其中深證成指股票指數(shù)命名為“SZA”，上證指數(shù)命名為“SHA”。實(shí)驗(yàn)步驟圖1SHA和SZA原始數(shù)值線性圖如圖1所示，粗略觀察可知，原始數(shù)據(jù)并不平穩(wěn)

2〕原始數(shù)據(jù)直方圖檢驗(yàn)圖2SHA原始數(shù)值直方圖圖3SZA原始數(shù)值直方圖由圖2、圖3所示，JB統(tǒng)計(jì)量的值較大且不趨近于0,圖像不符合正態(tài)分布，說(shuō)明數(shù)據(jù)不平穩(wěn)3〕原始數(shù)據(jù)ADF檢驗(yàn)

NullHypothesis:SHAhasmunitrootExogenous:ConstantLagLength:4[Automatic-basedonS-IC,maxlag=21:t-StatisticProb.*AugmentedDickey-Fullerteststatistic-1.4374540.5650Testcriticalvalues:1%level5%level10%level-3.436703-2S64233-2.56S256*MacKinnon(1996)one-sidedp-valuesAugmentedDickey-FullerTestEquationDependentVariable:D(SHA)Method:LeastSquaresDate:05；16/13Time:15:39Sample(adjusted):61000Includedobservation.s:995afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.}-Q.OO++U4-0.003064-1.43-74640.1509D(SHA(-1D0.1033360.0314543,4443150.0006D(SHAf-2))-0.0367-190,031633-2.7409&40.0062D(SHA[-3)}0.02061100316230.65-17^-10.5147D(SHAH))0.1558320.0314664.95-2^90.0000C12.997599.76618313308770.1835R-squared0.045871Meandependsntvar-1.030000AdjustedFt-squa.red0.0410^7S.D.dependentvar54.766B3SE.ofregression53.63103Akaikeinfocriterion10.80814圖4SHA原始數(shù)值的ADF檢驗(yàn)結(jié)果NullHypothesis:SZAhasaunitrootExogenous:ConstantLagLength:1(ALtomatic-basedonS-IC,maxlag=21)t-StatisticPrab.^AugmentedDickey-Fullerteststatistic-1.6265100.4686Testcriticalvalues: 1%level-3.4366335%level-2.^6422510%level-2.56S251^MacKinnon(1996)one-sidledp-valuesAugmentedDickey-FullerTestEquation□ependentVariable:D(SZA>Method;Square□ate:05/16/1STime:15:51Sample(adjusted}:3-1000Includedobservation.s:998afteradjustmentsVariableCoefTicientStd.Errort-&tatisticProb.SZA[-1)-0.0057820.003555 -1.6265100.1042□[SZAC-m0.1056710.031566 3.3475710.0003C58.725393S.33986 1.5297110.1264R-squared0013063Meandependentvar-3-.1U494AdjustedR-squared0.011079S.D.dependentvar209.U03S.E.ofregression207.9785Akaikeinfocriterion13.51575Sumsquaredresid4303S79&Schwarzcriterion13.5對(duì)5。Loglikelihood-6741.358Hannan-Ciuinncriter.13.52135F-3tatistic6.584638Durbin-Watsonstat1.986906Prob(F-statistjc)0.001442圖5SZA原始數(shù)值的ADF檢驗(yàn)結(jié)果由圖4、圖5可知，原始數(shù)據(jù)均未能通過(guò)ADF檢驗(yàn)，拒絕SHA、SZA具有單位根的原假設(shè)。此時(shí)應(yīng)對(duì)數(shù)據(jù)取對(duì)數(shù)，再對(duì)新變量進(jìn)行平穩(wěn)性檢驗(yàn)。點(diǎn)擊Eviews中的“quick”一"generateseries”鍵入logsha=log(sha),同樣的方法得到logsza。此時(shí)，logsha和logsza為新變量，對(duì)其進(jìn)行平穩(wěn)性檢驗(yàn)方法如上，發(fā)現(xiàn)也是不平穩(wěn)的。5〕修正數(shù)據(jù)折線圖檢驗(yàn)

圖6logSZA和logSHA的線性關(guān)系圖7〕修正數(shù)據(jù)ADF檢驗(yàn)用ADF方法檢驗(yàn)logsha和logsza的平穩(wěn)性。通過(guò)比較檢驗(yàn)值和不同顯著性下的關(guān)鍵值來(lái)得出結(jié)論。如圖對(duì)logSHA檢驗(yàn)結(jié)果中所示，檢驗(yàn)值小于關(guān)鍵值，發(fā)現(xiàn)數(shù)據(jù)是不平穩(wěn)的。AugmentedDicKev-Fullerteststatist!c-0.5944080.8S92Testcriticalvalues: 1%level5%level10%level^MacKinnon(1996)one-sidedp-values.-3.436676-2.864222-2.56S2&0AugmentedDiclcey-FuIlerTestEquationDependlentVariaWe:DfLOGSHA)Method:LeastSquares□ate:05/16/18Time:11:28Sample(adjusted):21000Includedobservations:999afteradjustmenisVariableCoefficientStd.Errort-StaiisticProbLOGSHAt-1)-0.0016030.002697 -0.59440S0.5524C0.01247S0.021676 0.5756660.5650R-squared0.000354Meandependentvar-0.000403AdjustedR-squared-0.000648S.D.dependentwar0.015548S.E.ofregression0.015554AkaiKeinfocriterion-5.487058Sumsquaredre^id0.241187Schwarzcriterion-5.477235Laglikelihood2742785Hannan-Quinncriter.-5.403324F-statistic0,353321Durbin-Watson汨1.851141Prob(F-staiistic)0.552374圖6logSHA的ADF檢驗(yàn)結(jié)果

如圖7所示，在進(jìn)一步對(duì)logSZA檢驗(yàn)中，發(fā)現(xiàn)檢驗(yàn)值小于關(guān)鍵值，說(shuō)明數(shù)據(jù)也是不平

穩(wěn)的。NullHypothesis:LOGSZAhasmunitrootExogenous:Consta.nlLagLength:0(Automatic-basedonSIC,maxlag=21)t-StatisticProb/AugmentedDickey-Fullerteststatistic-1.0948130.71&&Testcriticalvalues: level5%level10%level-3.436676-2.064222-2.56S25-0^MacKinnon(1996)one-sided|>values.AugmentedDickey-FullerTe^tEquation□ependlentVariable:D(LOGSZA>Method:LeastSquaresDate;0^16/18Time;1132Sample(adjusted):21000Includedobservations:999afterac^ustmentsVariableCoefficient&td.Errort-StatisticProb.LOGSZA[-1)-0.00J&950.00^284 -1.0S481J0.2739C0.0329280.030403 1.0B30540.2790R-squared0.001201Meandependentwar-0.000352AdjustedFl-sqjaredO.OOO199S.D.dependentvar0.017858S.E.ofregre-ssion0.017856Akaikeinfocriterion-5.210967Sumsquaredresid0.317S76S