時(shí)間序列分析課后習(xí)題答案1

時(shí)間序列分析后習(xí)題案（上機(jī)）第二章2、342340338336334332330328197519761978

19791980（1）時(shí)序圖如上：序列具有明顯的趨勢(shì)和周期性，該序列非平穩(wěn)。（2）樣本自相關(guān)系數(shù)：（3）該樣本自相關(guān)圖上，自相關(guān)系數(shù)衰減為的速度緩慢，且有正弦波狀，顯示序列具有趨勢(shì)和周期，非平穩(wěn)。3）樣本自相關(guān)系數(shù)：word檔可自由復(fù)制編輯

（2）序列平穩(wěn)。（3）Q統(tǒng)計(jì)量對(duì)應(yīng)的概率均大于0.05，故接受該序列為噪聲的假設(shè)，即序列為村隨機(jī)序列。5）時(shí)序圖和樣本自相關(guān)圖：3503002502001501005000:0100:0701:0101:0702:0102:0703:0103:07Xword檔可自由復(fù)制編輯

（2）序列具有明顯的周期性，非平穩(wěn)。（3）序列的Q計(jì)量對(duì)應(yīng)的概率均小于，該序列是非白噪聲的。6）word檔可自由復(fù)制編輯

根據(jù)樣本相關(guān)圖可知：該序列是非平穩(wěn)，非白噪聲的。（2）對(duì)該序列進(jìn)行差分運(yùn)算yxtt{y}樣本相關(guān)圖：t

t該序列平穩(wěn)，非白噪聲。第三章：

1word檔可自由復(fù)制編輯

結(jié)論：序列平穩(wěn)，非白噪聲。（2）擬合MA(2)model:VariableCMA(1)MA(2)

Coefficient80.405680.3367830.343877

Std.Error4.6303080.1146100.116874

t-Statistic17.365082.9385192.942297

Prob.0.00000.00470.0046R-squared

0.171979Meandependentvar80.29524AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedMARootsResidual

0.144379S.D.dependentvar21.94078Akaikeinfocriterion28883.87Schwarzcriterion-282.4221F-statistic2.072640Prob(F-statistic)-.17+.56i-.17-.56i

23.719819.0610199.1630736.2309760.003477（）擬合AR(2)model：VariableCAR(1)

Coefficient79.719560.258624

Std.Error5.4426130.128810

t-Statistic14.647292.007794

Prob.0.00000.0493word檔可自由復(fù)制編輯

AR(2)R-squared

0.2274690.1251141.8181020.07420.154672Meandependentvar79.50492AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsResidual

0.125522S.D.dependentvar21.83590Akaikeinfocriterion27654.79Schwarzcriterion-273.1140F-statistic1.939572Prob(F-statistic).62-.36

23.350539.0529189.1567315.3061950.007651(4)擬合，1）：VariableCAR(1)AR(2)MA(1)

Coefficient79.17503-0.5868340.3761201.113999

Std.Error4.0829080.1180000.0820910.097122

t-Statistic19.39183-4.9731704.58175611.47012

Prob.0.00000.00000.00000.0000R-squared

0.338419Meandependentvar79.50492AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodword檔可自由復(fù)制編輯

0.303599S.D.dependentvar19.48617Akaikeinfocriterion21643.51Schwarzcriterion-265.6386F-statistic

23.350538.8406118.9790299.719104

Durbin-WatsonstatInvertedARRootsInvertedMARoots殘差檢驗(yàn)：

1.963688Prob(F-statistic).39-.97-1.11EstimatedMAprocessisnoninvertible

0.000028（）擬合12）model:VariableCAR(1)MA(2)

Coefficient79.521000.2705060.233914

Std.Error4.6219100.1256060.130773

t-Statistic17.205232.1536031.788701

Prob.0.00000.03540.0788R-squared

0.157273Meandependentvar79.55161AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRoots殘差檢驗(yàn)：

0.128706S.D.dependentvar21.61946Akaikeinfocriterion27576.65Schwarzcriterion-276.9995F-statistic1.981887Prob(F-statistic).27

23.161269.0322429.1351675.5053860.006423word檔可自由復(fù)制編輯

(6)化modelMA(2)AR(2)ARMA(2，1)ARMA(1,（2）)

AIC9.06109.05298.84069.0322

SC9.16319.15678.97909.1352根據(jù)SC準(zhǔn)則，最優(yōu)模型為ARMA(2,1)模型。(7)測(cè)：年份

預(yù)測(cè)值

標(biāo)準(zhǔn)差

95％的置信下限95％的置信上限19641965196619671968

83.8063088.0511475.7081584.5480074.71802

19.4861722.0280122.0663922.2831122.32277

45.6134144.8762432.4580340.8731030.96539

121.9992131.226118.9583128.2229118.4706word檔可自由復(fù)制編輯

18）平穩(wěn)性判斷與純隨機(jī)性檢驗(yàn)：序列平穩(wěn)，非白噪聲。（）擬合）model:VariableCAR(1)

Coefficient0.8454410.372564

Std.Error0.0520130.111569

t-Statistic16.254273.339322

Prob.0.00000.0013R-squared

0.135739Meandependentvar0.849589AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRoots殘差檢驗(yàn)：

0.123566S.D.dependentvar0.278633Akaikeinfocriterion5.512162Schwarzcriterion-9.284669F-statistic2.068675Prob(F-statistic).37

0.2976270.3091690.37192111.151070.001341word檔可自由復(fù)制編輯

（）擬合）model:VariableCMA(1)MA(2)MA(4)MA(6)

Coefficient0.8372700.2018530.3011180.2785660.270084

Std.Error0.0656410.1102890.1048140.1105280.115984

t-Statistic12.755261.8302252.8728752.5203222.328636

Prob.0.00000.07150.00540.01400.0228R-squaredAdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.189662Meandependentvar0.142686S.D.dependentvar0.273989Akaikeinfocriterion5.179833Schwarzcriterion-6.607637F-statistic1.867536Prob(F-statistic)

0.8512160.2959130.3137200.4694004.0374200.005328InvertedMARoots殘差檢：

.61+.50i.61-.50i-.04-.77i-.04+.77i-.68+.53i-.68-.53iword檔可自由復(fù)制編輯

（）擬合ARMA((2),1)modelVariableCAR(2)MA(1)

Coefficient0.8522990.2607380.452777

Std.Error0.0612550.1237110.117596

t-Statistic13.913902.1076403.850279

Prob.0.00000.03870.0003R-squared

0.219781Meandependentvar0.855139AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsInvertedMARoots殘差檢：

0.197166S.D.dependentvar0.265118Akaikeinfocriterion4.849841Schwarzcriterion-5.045646F-statistic2.041391Prob(F-statistic).51-.51-.45

0.2958870.2234900.3183519.7183460.000191word檔可自由復(fù)制編輯

（）優(yōu)化modelAR(1)MA(6)ARMA((2)，1)

AIC0.30920.31370.2235

SC0.37190.46940.3184根據(jù)SC準(zhǔn)則，最優(yōu)模型為ARMA((2),1)模型。(6)測(cè)：年份

預(yù)測(cè)值

標(biāo)準(zhǔn)差

95％的置信下限95％的置信上限19751976197719781979

0.647740.750010.798960.825630.83839

0.265120.291030.299120.300760.30130

0.128100.179600.212680.236150.24785

1.167371.320421.385241.415111.42893word檔可自由復(fù)制編輯

18.(1)序列平，非白噪聲（）擬合）模型VariableCAR(1)AR(2)AR(3)

Coefficient84.13028-0.395022-0.298634-0.186335

Std.Error0.1003700.0704600.0726520.070027

t-Statistic838.2004-5.606293-4.110476-2.660918

Prob.0.00000.00000.00010.0084R-squared

0.161289Meandependentvar84.12980AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedARRootsword檔可自由復(fù)制編輯

0.148320S.D.dependentvar2.655132Akaikeinfocriterion1367.647Schwarzcriterion-472.2752F-statistic2.001728Prob(F-statistic).06-.60i.06+.60i-.52

2.8770534.8108614.87729112.435810.000000

殘差檢：（）擬合AR(1,2,3,6)型：VariableCAR(1)AR(2)AR(3)AR(6)

Coefficient84.14284-0.395527-0.304273-0.1818640.148199

Std.Error0.1087890.0707540.0734400.0706240.065240

t-Statistic773.4515-5.590134-4.143128-2.5751102.271609

Prob.0.00000.00000.00010.01080.0242R-squared

0.186539Meandependentvar84.13128AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.169414S.D.dependentvar2.633285Akaikeinfocriterion1317.496Schwarzcriterion-462.9657F-statistic1.985492Prob(F-statistic)

2.8893864.7996484.88357110.892510.000000InvertedARRootsword檔可自由復(fù)制編輯

.59.27-.71i.27+.71i-.37-.64i-.37+.64i-.79

殘差檢：（）擬合）模型VariableCMA(1)

Coefficient84.13042-0.480740

Std.Error0.0990450.062375

t-Statistic849.4201-7.707312

Prob.0.00000.0000R-squared

0.148110Meandependentvar84.11940AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-WatsonstatInvertedMARoots殘差檢：

0.143830S.D.dependentvar2.689485Akaikeinfocriterion1439.433Schwarzcriterion-483.0610F-statistic1.872891Prob(F-statistic).48

2.9066254.8264774.85934634.598330.000000word檔可自由復(fù)制編輯

（）擬合ARMA((1),(1,6))模型：VariableCAR(2)MA(1)MA(6)

Coefficient84.11553-0.167970-0.3751340.168123

Std.Error0.1269430.0745650.0687390.065812

t-Statistic662.6253-2.252656-5.4573762.554578

Prob.0.00000.02540.00000.0114R-squared

0.175501Meandependentvar84.10402AdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodDurbin-Watsonstat

0.162816S.D.dependentvar2.646779Akaikeinfocriterion1366.061Schwarzcriterion-474.0437F-statistic2.001830Prob(F-statistic)

2.8927264.8044604.87065713.835720.000000InvertedMARoots殘差檢：

.72-.36i.72+.36i.06+.73i.06-.73i-.59-.37i-.59+.37iword檔可自由復(fù)制編輯

（）擬合ARMA(3(6))模：VariableCAR(1)AR(2)AR(3)MA(6)

Coefficient84.12708-0.388317-0.320461-0.183