季節(jié)性時間序列實驗報告

時間序列分析實驗報告——季節(jié)性時間序列時間序列分析實驗報告［一］實驗?zāi)康氖煜ふ莆占竟?jié)性時間序列模型的識別、建立、參數(shù)估計、適應(yīng)性檢驗以及模型預(yù)測的原理，掌握數(shù)據(jù)平穩(wěn)化處理的方法以及判斷方法，熟悉四種模型定階的方法及其原理，掌握適應(yīng)性檢驗的方法。［二］實驗準(zhǔn)備學(xué)習(xí)實驗中要用到的的方法，準(zhǔn)備數(shù)據(jù).1、數(shù)據(jù)：1946-1970年美國各季生產(chǎn)者耐用品支出資料。數(shù)據(jù)如下:時季支出時季支出時季支出1946.17.501947.115.501948.118.001946.28.901947.215.701948.217.401946.311.101947.315.601948.317.901946.413.401947.416.701948.418.801949.117.601950.115.901951.120.201949.217.001950.217.901951.220.501949.316.101950.320.301951.320.901949.415.701950.420.401951.420.901952.121.101953.121.401954.120.401952.221.401953.221.301954.220.401952.318.201953.321.901954.320.701952.420.101953.421.301954.420.701955.120.901956.125.601957.128.101955.223.001956.226.101957.228.001955.324.901956.327.001957.329.101955.426.501956.427.201957.428.301958.125.701959.127.001960.129.601958.224.501959.228.701960.231.201958.324.401959.329.101960.330.601958.425.501959.429.001960.429.801961.127.601962.131.001963.133.201961.227.701962.232.101963.233.801961.329.001962.333.501963.335.50

1961.430.301962.41964.137.901965.11964.239.001961.430.301962.41964.137.901965.11964.239.001965.21964.341.001965.31964.441.601965.41967.153.901968.11967.255.601968.21967.355.401968.31967.456.201968.41970.164.801970.265.601970.367.201970.462.1033.201963.436.8043.701966.150.2044.401966.252.1046.601966.354.0048.301966.456.0057.901969.163.1057.301969.263.5058.801969.364.8060.401969.465.701）操作方法（單位根檢驗、數(shù)據(jù)零均值化、作圖、差分、模型回歸、ACF與PACF）。2）理論部分通過觀察ACF和PACF判斷模型形式------模型識別ACF、PACF方法定階-殘差方差圖法定階"模型定階F檢驗定階法/OLS估計參數(shù)估計相關(guān)系數(shù)檢驗法適應(yīng)性檢驗卡方檢驗法模型預(yù)測方法［三］實驗過程及內(nèi)容一、數(shù)據(jù)處理：樣本數(shù)據(jù)樣本容量為100.1、輸入樣本y1）作圖可見數(shù)據(jù)有長期趨勢口T-,=EiJTJ|EWatidle|：*?!-_-HrlnHWHF2ES222)單位根檢驗，根據(jù)P值和t值可看出數(shù)據(jù)是不平穩(wěn)的NullHypothesis:YhasaunitrootExogenous:NoneLagLength:0(AutomaticbasedonSIC,MAXLAG=11)t-StatisticProb.*AugmentedDickey-Fullerteststatistic5.1164691.0000Testcriticalvalues:1%level-2.5892735%level-1.94421110%level-1.614532*MacKinnon(1996)one-sidedp-values.做一階差分得到"1,并且零均值化。對y1進(jìn)行單位根檢驗，結(jié)果數(shù)據(jù)是平穩(wěn)的。NullHypothesis:Y1hasaunitrootExogenous:NoneLagLength:0(AutomaticbasedonSIC,MAXLAG=11)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-6.2385710.0000Testcriticalvalues:1%level-2.5895315%level-1.94424810%level-1.614510作圖可以看到仍有周期性1□10-26302531□10-2630253&毆0B09!12口晞0036r?262。色I(xiàn)1|130014HtHB7?446口戚H1.日面J)(SS9.H31O.Effi1]|50O4EDOSE目阿0.137|11GNimtME&3SK9怕1|F7D119D136??Q50J96□1"1320311K7(H第1□5OC0601S4”酰020?11：Ifi008300OB口頌0.2391|?11網(wǎng)1勺D(M00.3M1r12DOS?D04)13W40Sff1.i13OflID□庠壯9住。.斕1HU01?0060>52050361111；悟0CI6001815弊043S11|i16MHf-0020昉借04鴕|II1?典D11B1N750.490淄|!IB-D1OB16.7E40.5M1Bi190V8QD11D17J8Q0.-536i120DffiJD03E怕.叫0577C1V-0078-015S扭或60.590111；H-01?』053測橙口吸11239111-005622CH05201t2JoniS0029歸.他瀕11X-DQ324)007&昭Q碰1t志D04B-DII3E22日ROtEi11H-iOin-OMO07031h15000：i0032226660.750111?0C?9-0&H29S460751C!胡們耕-02262533&40561■|亟PUKtEfE13■1e—奉!dJ?j目,*&.g—：yjF1此iimci-壬職on間Ffer，^■mth1^H5fTtol-分析acf和pacf發(fā)現(xiàn)仍有季節(jié)性16wnm■*■!rm■ew.rarm'l：,￡?Sag*I9UGQ1IM1W脾In血場qgc■向郵巍'：酒云；畿3加iQCEd就頃PaiUalConBlBti?iACPAC*SlilProbKtEZr^J目］七口巨］＜1皿UJ2、剔除周期因素令y4=y-y(-4)，零均值化后y4_0作圖觀察發(fā)現(xiàn)仍有周期性

OPrf*丹11AEOgciws^prdcwi|j-r!p,E；Wagea；MarteSan^S舊峽出!圮財,單位根檢驗發(fā)現(xiàn)序列已經(jīng)平穩(wěn)了NullHypothesis:Y4_0hasaunitrootExogenous:NoneLagLength:0(AutomaticbasedonSIC,MAXLAG=11)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-7.3204030.0000Testcriticalvalues:1%level-2.5895315%level-1.94424810%level-1.614510*MacKinnon(1996)one-sidedp-values.再對y4做一階差分得到y(tǒng)4_1再對其做零均值化得y4_1_0單位根檢驗結(jié)果說明序列y4_1_0是平穩(wěn)的，畫圖發(fā)現(xiàn)周期性已剔除。NullHypothesis:Y4_1_0hasaunitrootExogenous:NoneLagLength:3(AutomaticbasedonSIC,MAXLAG=11)

t-StatisticProb.*AugmentedDickey-Fullerteststatistic-7.8464090.0000Testcriticalvalues:1%level-2.5906225%level

10%levelt-StatisticProb.**MacKinnon(1996)one-sidedp-values.□UleEditQbj?ctEtmSnichOitiihEJi-ndw山攻-1.944404-1.614417血園g|fku|D聞IPiotatiedFtirt|r<affw|Fr哽!艮仲|(zhì)&村卦院t|5Lats|[dentLin?|Ba~464850525456580062646668-1.944404-1.614417血園Y410Filh=t皿的1Lc.ArddoEuwiLE.Ifi=riin^￥F=y二、模型建立1、模型識別通過觀察ACF和PACF的截尾、拖尾情況來初步確定模型形式，可分為三種情況：ACF拖尾，PACF截尾的情況初步認(rèn)定為AR模型ACF截尾，PACF拖尾的情況初步認(rèn)定為MA模型ACF、PACF均拖尾的情況初步認(rèn)定為ARMA模型PilaEditDbjsctViaEtic|nick酗血liiiiwNdp■品:i歐K_：_DFtrkfih:I：：ButIetI^.□X|成|祠口腳I啊Htis|FTitl險1仙此河|為晡|國巾拂址5|漩|此|討|何佰嗔||嫌用_1』嗣祠的jaiFlirt軸e由;EI涮'間』幽F〕〕l匚1-1'?.二點(diǎn).項....1二1:-：：:::11:1:：：：■■：：：：：21I二[1匚1J-DJOE6J.23115.503Q0W1II1:1:D.1IEm16WQOffi[111匚11||"三：衛(wèi)二「；二'匚11II■|[11"二:E*1：：：：9D.12??31.143QODO1:111：〕三頊二二11||II111111-DJOEEW35.120QODO：「"二1111\二，二E-6:1-二1II11-壬0.DO6-8'0-QODO1111II1II111II■:<1:史任：：："二二衛(wèi)/"夏:::■:二"二-』：2：:::匚11||||111"上成時：[二??：：』-E::"1]|1□I[.2廠配二二111111II21二三0.03348.5D6Q0Q1工二".尚』"1二.11||1II11111H?二二.F板壬二,L:七門1仃三二2：："：:hi苴:"1II1126DUffi0.D2653.160QOHI11111II1111□』.："：.￥<<二.29-DUSm泌3"二E二IU"二[1111II||13：：N：：/l：頂::"31?41.119K.D36QODO11111nnn?inn^nnm<c：j^ht：q-"i；、：：H：r\：-r-底litl：e'1!.iooneats戒sethnp^yraiiyikimalsIB：皿皿IIP=y分析ACF可以看作是截尾的，從第三階截尾，PACF是拖尾的，初步認(rèn)定是MA模型2、模型定階1)ACF、PACF方法:原理：Bartlett公式：當(dāng)k>q時，N充分大，pk的分布為漸進(jìn)正態(tài)分布N[0,-(1+2*p2)]由正態(tài)分布分布的3q原則可知道，下面等式近似成立1NiI'1=1/EPK舊良」+2!p)=683%P(IPKI^M|'1+虬P「)=95.45%*I=1對于每個q計算統(tǒng)計量：1+工

偵Np2,i=1對于每個q計算統(tǒng)計量：1+工

偵Np2,i=1并計算ACF從q+1到q+10的值中小于統(tǒng)計量的比例是否滿足條件。在此實驗中MA(q)k'N=10①當(dāng)q=1時，計算U從第1+1階到1+10階的值-0.059-0.009-0.0860.0980.106-0.1400?237-0?2720.1270.039p1=-0.380京1+2p「=0.227P(IPKP:I=1\--2N\：1+2^Pl2)=8/10=80%小于95.5%l=1A②當(dāng)q=2時，計算肉「從第2+1階到2+10階的值-0.0090.0980.106-0.1400?237-0?2720.1270.039-0.0860.087p2=-0.059土1+2工p2=M?'1+2(p2+p2=0.228：￡N弋i=]i10、12P(IpK|W』(1+位Pi2)=8/10=80%小于95.5%③當(dāng)q=3,4,5,6時同樣未達(dá)到95.9%的概率要求A當(dāng)q=7時，計算肉「從第7+1階到7+10階的值-0?2720.1270.039-0.0860.087-0.0920.125-0.082-0.0240.129P7=0.237P（IPK|W』J+位P「）=9/10=90%小于95.5%q=8時，計算肉U從第8+1階到8+10階的值0.1270.039-0.0860.087-0.0920.125-0.082-0.0240.129-0.181P8=-0.272號『+2工p；=0.256P（IpKI*號「+2^P「）=10/10=100%大于95.5%由ACF、PACF方法確定MA模型階數(shù)為82）殘差方差圖法：MA（q）原理：用統(tǒng)計量c；=&%來衡量模型的擬合優(yōu)度，該統(tǒng)計量越小說明擬合得越好。。a2=NQq，其中。=剩余平方和即殘差平方和q12345678910Q133.5149129.1999128.9904133.2097122.5560128.1216128.0930117.3417109.1160109.0761N-q99989796959493929190b21.3481.3181.3291.3871.2901.3631.3861.2751.1991.211根據(jù)殘差方差圖法，q=9時七2最小，因此確定MA模型的階數(shù)為9F檢驗定階法：通過兩個回歸模型的殘差平方和構(gòu)造F統(tǒng)計量，對兩個模型進(jìn)行檢驗，判斷兩個回歸模型是否具有顯著性差異，即一模型是否顯著優(yōu)于二模型。該實驗的檢驗中r=9,s=1,MA(9)回歸得到殘差平方和Qo=109.1160舍棄1個變量得到MA(8)模型，回歸得到Q1=117.3417=6.86F統(tǒng)計量.(g-Q0)/1=(117.3417-109.1160)/1=6.86"°109.1160/N-9F(1，91)在a=0.05時的臨界值為3.92，F(xiàn)統(tǒng)計量為6.86大于3.92，因此拒絕原假設(shè)。說明兩個回歸模型是有顯著性差異的，最優(yōu)模型為MA(9).4)模型的具體確定：通過參數(shù)的顯著性t檢驗，剔除系數(shù)不顯著的變量初始樣本回歸模型中^4_1_0=0；ma(1)+氣ma(2)+仔ma(3)+0ma(4)+0ma(5)+0ma(6)+0ma(7)+0ma(8)+0ma(9)3456789Coefficient-StatisticProb.VariabletStd.ErrorMA(1)-0.6635170.101635-6.5284170.0000MA(2)-0.2523990.120477-2.0949940.0391MA(3)-0.0588040.122250-0.4810160.6317MA(4)-0.0513350.121769-0.4215770.6744MA(5)0.1169380.1212090.9647630.3374MA(6)-0.0048860.122905-0.0397540.9684MA(7)0.1482600.1217311.2179260.2266MA(8)-0.2717880.121426-2.2382990.0278MA(9)0.3480360.1035763.3601830.0012回歸結(jié)果中MA(6)的系數(shù)很不顯著，所以剔除MA(6)

MA(3)-0.0586600.121528-0.4826910.6305MA(4)同樣再剔除MA(3)、-0.052120MA(4)0.118205-0.4409340.6604MA(5)再剔除MA(5)0.0657280.0979810.6708240.5041Coefficient-StatisticProb.VariabletStd.ErrorMA(1)-0.6755420.092882-7.2730990.0000MA(2)-0.2750120.102206-2.6907670.0085MA(7)0.1974680.1035521.9069430.0597MA(8)-0.2812370.115473-2.4355180.0168MA(9)0.3437450.1030703.3350590.0012R-squared0.421526Meandependentvar-9.35E-18AdjustedR-squared0.395816S.D.dependentvar1.423116S.E.ofregression1.106177Akaikeinfocriterion3.090893Sumsquaredresid110.1265Schwarzcriterion3.225308Loglikelihood-141.8174Durbin-Watsonstat1.980577至此模型參數(shù)都較為顯著，確定模型為含有ma(1)、ma(2)、ma(7)、ma(8)、ma(9)的9階滑動平均模型：列_1_0=o；ma(1)+oAma(2)+@Ama(7)+00ma(8)+bma(9)2789三、模型參數(shù)估計OLS估計：對于MA模型Z=a-0a-0a--0att1t-12t-2qt-q{at}是零均值，同方差，獨(dú)立序列，因此可以用OLS估計對于本實驗的MA(9)進(jìn)行最小二乘估計結(jié)果VariableCoefficientStd.Errort-StatisticProb.MA(1)-0.6755420.092882-7.2730990.0000MA(2)-0.2750120.102206-2.6907670.0085MA(7)0.1974680.1035521.9069430.0597MA(8)-0.2812370.115473-2.4355180.0168MA(9)0.3437450.1030703.3350590.0012R-squared0.421526Meandependentvar-9.35E-18AdjustedR-squared0.395816S.D.dependentvar1.423116S.E.ofregression1.106177Akaikeinfocriterion3.090893Sumsquaredresid110.1265Schwarzcriterion3.225308Loglikelihood-141.8174Durbin-Watsonstat1.980577可以得到各個系數(shù)的估計值：0'1=-0.663517氣=-0.275012省宵宵07=0.19746808=-0.28123709=0.343745四、模型適應(yīng)性檢驗相關(guān)系數(shù)檢驗法對殘差項進(jìn)行相關(guān)系數(shù)檢驗，計算其ACF并比較大小。發(fā)現(xiàn)ACF的值都很小，說明殘差項沒有序列相關(guān)性c-°01ZI

雎騷酬?本溟gtsmnE二VZ6T0口OEd2+..?????+-ded3*44煽M44o6COo5oZgoCDmLgdbMgoCXIu)goLSOO'OIL.OV6nEoTnEvnl器更平(I1-ihjI■日li昂.^rirfwp1lhiiihnrininiB]ii?^■?ti111ticrn11v!Silffll!POBIIsSSfl■IM[UI11Ul岬■IL1lil坪IIUjIKAIUIHI岬HJ1MUJI!■UlIUWlHi1131U■■'Ul日坪岬呼呼■kl■設(shè)，｛七｝是獨(dú)立的，沒有序列相關(guān)性。5、預(yù)測數(shù)據(jù)的時間拓展兩期（兩個季度）workfile—proc—structrue然后進(jìn)行預(yù)測,forecast預(yù)測結(jié)果:丫1頃|F~u：uidHiAiLacfLsTXiA-F-lc-=UFruhaDE-djchIT=uaLiil/id可以看