2023年實(shí)驗(yàn)報(bào)告時(shí)間序列

實(shí)驗(yàn)報(bào)告

——平穩(wěn)時(shí)間序列模型的建立

08經(jīng)濟(jì)記錄

160814030

王思瑤

實(shí)驗(yàn)?zāi)康?/p>

從觀(guān)測(cè)到的化工生產(chǎn)過(guò)程產(chǎn)量的70個(gè)數(shù)據(jù)樣本出發(fā)，通過(guò)對(duì)模型的辨認(rèn)、模型的定價(jià)、模

型的參數(shù)估計(jì)等環(huán)節(jié)建立起適合序列的模型。

以下是化工生產(chǎn)過(guò)程的產(chǎn)量數(shù)據(jù):

obsBFobsBF

1473658

2643745

3233854

4713936

5384054

6644148

7554255

8414345

9594457

10484550

11714662

12354744

13574864

14404943

15585052

16445138

17805259

18555355

19375441

20745553

21515649

22575734

23505835

24605954

25456045

26576168

27506238

28456350

29256460

30596539

31506659

32716740

33566857

34746954

35507023

可以明顯看出序列均值顯著非零，所以用樣本均值作為其估計(jì)對(duì)序列進(jìn)行零均值化。

obsBF零均值化后的數(shù)據(jù)YobsBF零均值化后的數(shù)據(jù)Y

147-4.1285736586.87143

26412.871433745-6.12857

323-28.1285738542.87143

47119.871433936-15.12857

538-13.1285740542.87143

66412.871434148-3.12857

7553.8714342553.87143

841-10.128574345-6.12857

9597.8714344575.87143

1048-3.128574550-1.12857

117119.87143466210.87143

1235-16.128574744-7.12857

13575.87143486412.87143

1440-11.128574943-8.12857

15586.8714350520.87143

1644-7.128575138-13.12857

178028.8714352597.87143

18553.8714353553.87143

1937-14.128575441-10.12857

207422.8714355531.87143

2151-0.128575649-2.12857

22575.871435734-17.12857

2350-1.128575835-16.12857

24608.8714359542.87143

2545-6.128576045-6.12857

26575.87143616816.87143

2750-1.128576238-13.12857

2845-6.128576350-1.12857

2925-26.1285764608.87143

30597.871436539一12.12857

3150-1.1285766597.87143

4

327119.87143670-11.12857

33564.8714368575.87143

347422.8714369542.87143

3550-1.128577023-28.12857

二.實(shí)驗(yàn)環(huán)節(jié)

1.模型辨認(rèn)

零均值平穩(wěn)序列的自相關(guān)函數(shù)與偏相關(guān)函數(shù)的記錄特性如下:

模型AR(n)MA(m)ARMA(n,m)

自相關(guān)函數(shù)拖尾截尾拖尾

偏自相關(guān)函數(shù)截尾拖尾拖尾

所以，作零均值化后數(shù)據(jù)的自相關(guān)函數(shù)與偏自相關(guān)函數(shù)圖

Date：04/25/11Time:22:35

Sample:20232070

Inc1udedobservations:7o

Partia1Co

Autocorrelationrre1ationACPACQ-StatProb

-0.3

|***|.|10.3828210.6380.001

.ri.1**120.3250.20918.4440.000

.1.0.0121.23

**i.?13-0.193840.000

.r.i.I.140.090-0.04921.8570.000

-0.16-0.1

.*i-i.*l.1522623,9000.000

0.010.0

.i.i.*l.164-0.09423.91601

0.06

.i.i-1.170.012523.9280.001

-0.0-0.00.00

?*i.i.*1.18857924.5192

0.03-0.02

.?.i.I.199514.6440.003

.i.i.I*.1100.0330.08024.7360.006

.r.i.I*.1110.0900.12525.4260.008

-o.o

.*i.i.1.I12770.05425.9420.011

1-0.0

.i.i.1.130,0634526.2910.016

0.050.126.520.02

.i.i.I*.11413442

-0.020.03

.i.i.I*.115060.0796.5283

.i.I*.1160.1260.14528.0160.031

1-0.092

.*i.?.1.170-0.0408.7920.036

28.8

.i.i.1180.017-0.084200.051

-0.09-0.029.7

*l.I-I.I19917950.054

0.00—

I-I.I.I2060.03629.7980.073

0.010.050.09

I-I.I.|215529.8206

2-0.010.11

I-I-I-I2-0.037529.9689

I.I.I.|230.013-0.05129.9850.150

I.I.I.|240.0100.01029.9970.185

—30.020.22

I.I.I.|250.0150.01633

20.0330.10.26

I.I.I.I660.023721

2-0.01

I.I.I.|76-0.03630.2020.305

0.00.34

I.I.I.128330.03030.3357

2-0.05-0.03

I-I-I-I97150.7350.378

0.4

I-I.I.|300.051-0.00331.06412

3-0.0-31.70

1.1.1.11700.05360.431

1.—32.14

.I.|320.0570.00310.460

由上圖可知AutocorrelationPartia1Correlation序列均有收斂到零的趨勢(shì),可以認(rèn)

為Y的自相關(guān)函數(shù)與偏自相關(guān)函數(shù)均是拖尾的，所以初步判斷該序列適合ARMA模型。

2.模型定階

(1)根據(jù)Pandit?Wu建模方法，擬建ARMA(2,1)模型，在EViews命令欄中輸入：

LSYAR(1)AR(2)MA(1),得到如下結(jié)果：

DependentVariabIe：Y

Method:LeastSquares

Date:04/27/11Time:16：11

Samp1e(adjusted):20232070

Inc1udedobservations：68afteradjustments

Convergenceachievedafter16iterations

Backcast:2023

Coefft-Statisti

variableicientStd.ErrorcProb.

-0.837

AR(1)1280.327087-2.5593430.0128

-0.079-0.41665

AR(2)4100.19059020.6783

0.53136

MA(1)00.3171141.6756090.0986

0.2234Meandependent-0.128

R-squared30var570

AdjustedR-square0.1995S.D.dependent11.9713

d35var6

10.710Akaikeinfocrite

S.E.ofregression62rion7.623463

Sumsquared7456.6

resid29Schwarzcriterion7.721383

-256.1971.824

Log1ikelihood8Durbin-Watsonstat445

InvertedARR

oots-?11-.73

1nvertedMARoots一.53

令a2=resid,在Eviews命令行中輸入：genra2=resid再輸入：scata2

a2(-l)A看該模型的殘差與其滯后一期之間的散點(diǎn)圖：

30-

20-

10-

cT0-

-10-

-20-

-30-

-30-20-100102030

A2

從上圖看不出有相關(guān)趨勢(shì)，并且D.W值為1.824445,說(shuō)明不存在相關(guān)性,因此可以初步

認(rèn)為ARMA(2,1)模型是適應(yīng)的。

(2)根據(jù)Pandit-Wu建模方法，再建ARMA(4,3)模型，在EViews命令欄中輸入:

LSYAR(1)AR(2)AR(3)AR(4)MA(1)MA(2)MA(3),得到如下結(jié)果：

DependentVariab1e：Y

Method:LeastSquares

Date:04/27/11Time:16:36

Samp1e(adjusted):20232070

Includedobservations：66afteradjustments

Convergenceachievedafter191iterations

Backcast:20232023

Coeft-Statist

VariableficientStd.ErroricProb.

-0.598

AR(1)8740.145198-4.1245440.0001

0.312

AR(2)1000.1230012.5373790.0138

0.870

AR(3)9760.1186357.3416630.0000

0.174

AR(4)3630.1293781.3477020.1829

MA(1)0.3288360.0492186.6812140.0000

-0.288

MA(2)7470.056156-5.1418340.0000

0.05387

MA(3)-0.9400541-17.450060.0000

0.2367-0.00735

R-squared61Meandependentvar8

AdjustedR—squar0.1591

ed43S,D.dependentvar11.37949

Akaikeinfocriter7.62

S.E.ofregression10.43479ion8172

7.86040

Sumsquaredresid6424.210Schwarzcriterion9

-244.71.90732

Loglike1ihood297Durbin-Watsonstat7

InvertedARRoots.94-?22-.66-.64i-.66+.64i

-.6

InvertedMARoots.975+.74i-.65-74i

由上面結(jié)果可以看出：ARMA（4,3）模型的殘差平方和Sumsquaredresid為6424.21

0,ARMA(2,1)模型的殘差平方和Sumsquaredresid為7456.629,因此AR

MA(4,3)擬合效果更好;并且ARMA(4,3)模型的D.W值為1.907327,大于ARMA(2,1)

模型的D.W值1.824445,說(shuō)明ARMA(4,3)模型的擬合效果更好；RMA(4,3)模型

AIC值為7.628172,比ARMA(2,1)模型的7.623463稍大,但并不明顯。因此模型

ARMA(4,3)比模型ARMA(2,1)更好。

(3)根據(jù)Pandit-Wu建模方法，再建模型ARMA(6,5),在EViews命令欄中輸入:LS

YAR(1)AR(2)AR(3)AR(4)AR(5)AR(6)MA(1)MA(2)MA(3)MA(4)MA(5),

得到如下結(jié)果：

DependentVariable:Y

Method：LeastSquares

Date:04/27/11Time:16:46

SampIe(adjusted):20232070

Includedobservations:64afteradjustments

Convergenceachievedafter124iterations

Backcast:OFF(RootsofMAprocesstoolarge)

Coeffict—Statist

VariableientStd.ErroricProb.

0.21551

AR(1)0.15483830.7184610.4756

0.01906

AR(2)00.2076730.0917810.9272

AR(3)0.1427820.1214871.1752860.2451

AR(4)0.2354670.1697331.3872820.1712

AR(5)0.6786490.2092393.2434150.0020

0.11578

AR(6)40.1815760.6376610.5264

-0.61

MA(1)09750.318997-1.9153020.0609

0.5841.75188

MA(2)2470.33349700.0856

-0.105

MA(3)0150.308324-0.3406000.7348

-0.5608

MA(4)250.369143-1.5192630.1346

-1.160-2.69452

MA(5)5710.43071460.0094

Meandependent-0.0

R—squared0.596802var03570

AdjustedR—s0.5207211.3

quared7S,D.dependentvar2423

Akaikeinfocriter7.111

S.E.ofregression7.839709ion439

Sumsquaredres7.48249

id3257.435Schwarzcriterion7

-216.5Durbin-Watsonsta2.31

Loglikelihood661t8205

.28+.89.28-.89

InvertedARRoots1.07ii