2023年金融時(shí)間序列實(shí)驗(yàn)報(bào)告

。過釀《金融時(shí)間序列分析》綜合實(shí)驗(yàn)二金融系金融工程專業(yè)2023級姓名山洪國學(xué)號48實(shí)驗(yàn)地點(diǎn)：實(shí)訓(xùn)樓B305實(shí)驗(yàn)日期：2023.04.21實(shí)驗(yàn)題目：ARIMA模型應(yīng)用實(shí)驗(yàn)類型：基本操作訓(xùn)練實(shí)驗(yàn)?zāi)康模哼\(yùn)用美元對歐元匯率1993年1月到2023年12月的月均價(jià)數(shù)據(jù),進(jìn)行ARIMA模型的辨認(rèn)、估計(jì)、檢查及預(yù)測。實(shí)驗(yàn)內(nèi)容：1、創(chuàng)建Eviews文獻(xiàn)，錄入數(shù)據(jù)，對序列進(jìn)行初步分析。繪制美元對歐元匯率月均價(jià)數(shù)據(jù)折線圖,分析序列的基本趨勢，初步判斷序列的平穩(wěn)性。2、辨認(rèn)ARIMA(p,(1,口)模型中的階數(shù)口,(1,4。運(yùn)用單位根檢查(ADF檢查)擬定單整階數(shù)d;運(yùn)用相關(guān)分析圖擬定自回歸階數(shù)p和移動(dòng)平均階數(shù)q。初步選擇兒個(gè)合適的備選模型。3、ARIMA(p,d,q)模型的估計(jì)和檢查。對備選模型進(jìn)行估計(jì)和檢查,并進(jìn)行比較,從中選擇最優(yōu)模型。4、運(yùn)用最優(yōu)模型對2023年1月美元對歐元匯率的月均價(jià)進(jìn)行外推預(yù)測。評分標(biāo)準(zhǔn)：操作環(huán)節(jié)對的，結(jié)果對的，分析符合實(shí)際,實(shí)驗(yàn)體會真切。

實(shí)驗(yàn)環(huán)節(jié):1、根據(jù)所給的Exce1表格內(nèi)的數(shù)據(jù)，將表格內(nèi)的美元對歐元的匯率情況錄入到EViews9中，并對所錄入數(shù)據(jù)進(jìn)行圖形化的解決，所得到的圖形結(jié)果如下圖所示。（時(shí)間段：1993.01至2023.12)EUR/USD分析圖形數(shù)據(jù)可得，歐元對美元的匯率波動(dòng)情況較為明顯，其中在1999年至2023年期間歐元和美元的比值一度在1.0以上。但近些年以來,歐元的匯率一度連續(xù)下滑，到了2023年終的時(shí)候和和美元的比值在0.7左右。Date:04/19/17Time:17:00Sample:1993M012007M12Includedobservations:180AutocorrelationPartialCorrelationACPACQ-StatProbII109770977174760.000I匚I20.945-0.208339.270.000II□30.9180.120495.240.000II]I408940026644100.000III50.8720.014786.560.000III[I6O848-0.061922.070.000IjI]'708250.0421051.10.000IICI80.800-0.0931172.90.000II匚I90.770-0.0891286.50.000IIII100.739-0.0051391.80.000I?cI110.707-0.0891488.60.000II[I120672-0.0521576.70.000I11I130.638-0.0251656.50.000III140.6050.018172870.000III150.574-0.016179410.000III160.542-0.0221852.90.000I■I[I170.509-0.0331905.00.000IICI180473-0.0901950.20.000I-IrIIQC431-O1ARRnnnon如上圖所示，對前一?張圖的折線數(shù)據(jù)進(jìn)行了相關(guān)性分析，由圖中的Autocorrelation可知此數(shù)據(jù)為拖尾情況,說明它是非平穩(wěn)的。AugmentedDicKey-t-uiierunitMootIestonluk_usdNullHypothesis:EUR_USDhasaunitrootExogenous:ConstantLagLength:1(Automatic-basedonSIC,maxlag=13)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-1.1433840.6981Testcriticalvalues:1%level-3.4672055%level-2.87763610%level-2.575430*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(EUR_USD)Method:LeastSquaresDate:04/19/17Time:17:12Sample(adjusted):1993M032007M12Includedobservations:178afteradjustments再對此數(shù)據(jù)進(jìn)行單位根檢查,所得結(jié)果如上圖所示。VariableCoefficientStd.Errort-StatisticProb.EUR_USD(-1)-0.0140880.012321-1.1433840.2544d(eur1usd(-i?0.3190100.0720364.4284890.0000其中單位根檢查所相應(yīng)的P值為0.6981,遠(yuǎn)大于0.05的顯著性水平，因此可以說該序列是一個(gè)非平穩(wěn)序列。2、根據(jù)ARIMA模型，對該序列進(jìn)行一階的單位根檢查，如下圖>*uy?iivmvuuiiviuniti_unu，NullHypothesis:D(EUR_USD)hasaunitrootExogenous:ConstantLagLength:O(Automatic-basedonSIC.maxlaQ=13)^MacKinnon(1996)one-sidedp-values.t-StatistlcProb.-AuamentedDickey-Fullerteststatistic-9.67655500000Testcriticalvalues:1%level5%level1O%level-3.467205-2.877636-2575430AugmentedDickey-FullerTestEquationDependentVariable:D(EUR_USD.2)Method：LeastSquaresDate:04/19/17Time:17:24Sample(adjusted):1993M032007M12Includedobservations:178afteradjustments由該圖可知，對比前面的未一階差分的單位根檢查，此一階差分的單位根檢查p值為0小于顯著性水平0.05,因此拒絕原假設(shè),證明在一階差分下的序列數(shù)據(jù)才是平穩(wěn)的。因此VariableCoefficientStd.Errort-StatisticProbD(EUR_USD(-1))-0.6917210.071484-9.6765550.0000C-0.000638O001452-O439553O6608該序列的單整階數(shù)d為1eorreiogramoiM(tuK_u^u)Date:04/19/17Time:17:35Sample：1993M012007M12Includedobservations:179AutocorrelationPartialCorrelationACPACQ-StatProb1ZZ)1=)10.3080.30817.2790.000'□1匚12-0.087-0.20018.6490.000iE1113-0.115-0.02421.0710.00011114-0.0180.01721.1290.0001]l1)150.0760.06222.2180.0001111160.039-0.01622.5040.0011]l1JI70.0720.09523.4930.00113180.1270.10026.5690.0011Ji1190.0700.01427.5110.0011□1□100.1170.14430.1360.0011]>11110.0680.01531.0170.001111112-0.016-0.02031.0680.002111113-0.0220.00731.1600.0031[11[114-0.028-0.03331.3090.0051111150.007-0.01631.3180.0081111160.018-0.01731.3820.0121□13170.1290.12834.7140.0071Z]1]i180.1780.07541.0990.0011c?19-0.050-0.13941.6050.002如上圖所示，由于該序列的一階為平穩(wěn)的，所以作其一階相關(guān)性分析。從圖中可看出:自相關(guān)序列通過1期收斂于0.05區(qū)間內(nèi)，所以其移動(dòng)平均階數(shù)q的值為1,偏相關(guān)序列通過2階才變?yōu)?,則可知其自回歸階數(shù)p的值為2.綜上所述，可得：p=2；d=l;q=l初步適合EUR0的模型有:ARIMA(1,1,0)>ARIMA(2,1,0)、ARIMA(0,1,1)、ARIMA(1,1,1).ARIMA(2,1,1)3、對模型ARIMA(p,d,q)的估計(jì)與檢查

ViewProc]Object||Print?Name|FreezejEstimateForecastStats|ResidsDependentVariable:DEUR_USDMethod:LeastSquaresDate:04/21/17Time:18109Sample(adjusted):1993M032007M12Includedobservations:178afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientStd.Errort-StatisticProb.C-0.0009220.002097-0.4398900.6606AR(1)0.3082790.07148443125520.0000R-squared0.095572Meandependentvar-0.000886AdjustedR-squared0090433SDdependentvar0020291S.E.ofregression0.019352Akaikeinfocriterion-5.040911Sumsquaredresid0065909Schwarzcriterion-5.005160Loglikelihood4506411Hannan-Quinnenter-5.026413F-statistic18.59810Durbin-Watsonstat1.871573Prob(F-statistic)0000027InvertedARRoots.31如上圖所示，由于其中的截距項(xiàng)所相應(yīng)的t記錄量的Prob值為0.6606>0.05的顯著性水平，因此要剔除截距項(xiàng)c。ViewProcObject|PrintNameFreezeEstimate；ForecastStatsResidsDependentVariable:DEUR_USDMethod:LeastSquaresDate:04^1/17Time:18:16Sample(adjusted):1993M032007M12Includedobservations:178afteradjustmentsConvergenceachievedafter2iterationsVariableCoefficientStd.ErrorbStatisticProb.AR(1)0.3095220.0712654.3432280.0000R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.094579Meandependentvar-0.0008860.094579S.D.dependentvar0.0202910.019307Akaikeinfocriterion-5.0510500.065982Schwarzcriterion-5.033174450.5434Hannan-Quinncriter.-5.0438011.871488InvertedARRoots.31將截距項(xiàng)c去掉之后,在進(jìn)行回歸可得上圖所示的內(nèi)容。因此，根據(jù)圖內(nèi)的數(shù)據(jù)可知:Wt=0.309522W(t-1)t=4.343228單從P值來看的話，系數(shù)是顯著的。但是還要對殘差進(jìn)行白噪聲檢查[ViewjProc|Object1,PrintjName|Freeze|EstimateForecastIStats|ResidsCorrek)gramofResidualsDate:04/21/17Time:18:26Sample:1993M032007M12Includedobservations:178Q-statisticprobabilitiesadjustedfor1ARMAterm(s)AutocorrelationPartialCorrelationACPACQ-StatProbihi?b110.0620.0620.6943匚?□?2-0.163-0.1675.53180.019?C?id?3-0.108-0.0897.66300022111014-0.017-0.0337.71510.052I]l?pi50.0770.050881090.06611?i?6-0.003-0.0298.81250.1171I*,h70.0430.0639.16070.1651J?pi80.0990.10411.0210.13811)?9-0.0050.00111.0270.200?]??b100.0970.143128290171111iDi110.0430.05813.1890213111?I?12-0.033-0.00113.3990.268'11?|?13-0.0060.024134060.340如上圖所示，在對殘差項(xiàng)進(jìn)行Q檢查的時(shí)候，選擇K=l3,得到的Q檢查結(jié)果如如所示。在第13行數(shù)據(jù)中找到Q記錄量為13.406,其所相應(yīng)的相伴概率(Prob)為0.340>0.05,因此接受序列不相關(guān)的假設(shè)，即可認(rèn)為該殘差序列是白噪聲。然后，可用類似的方法對對之前所得到的其他四個(gè)模型ARIMA(2,1,0)、ARIMAS,1,1)、ARIMA(1,1,1)、ARIMA(2,1,1)進(jìn)行與之相應(yīng)的估計(jì)與檢查。通過了一系列的檢查之后，ARIMA(1,1,0)、ARIMA(2,1,0)、ARIMA(0,1,1)三個(gè)檢查都通過參數(shù)顯著性檢查、模型平穩(wěn)性、可逆性檢查、殘差序列白噪聲檢查。剩下的兩個(gè)模型ARIMA(1,1,1)、ARIMA(2,1,1)則并沒有通過檢查。MODEL①1R人2ProbARIMAC1,1,0.3090.09450.3400)ARIMA(2,1,0)0.354-0.2060.12450.6