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# 时间序列分析代考 MAT3375代写

2022-07-03 10:14 星期日 所属： 时间序列代写 浏览：57 ## Time: 2 hours

• ### This exam is open book and should be completed at home indepen-dently.

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### 1.Let yi.  N (β  , σ2),  for  i  =  1, 2, . . . , m  and  yi.  N (β1, σ2), for i =m + 1, m + 2, . . . , m + n.  时间序列分析代考

In other words the model

yi = β0 + si, i = 1, 2, . . . , m.

and

yi = β1 + si, i = m + 1, m + 2, . . . , m + n.

(i)Find M.L.E. for β0, β1and σ2.

(ii)Findthe distribution for βˆ0  and βˆ1.

(iii)Find an unbiased estimator for σ2

(iii) Explain how  to test the null  hypothesis

H0 : β0 = β1

against

H1 : β0 ƒ= β1.

### 2.The regression model  时间序列分析代考

yi = β0 + β1xi1 + β2xi2 + si, i = 1, 2, . . . , n = 19

with   i. N (0, σ2).  From  the  ouput  of  R  the  matrix  (X X)1 and  some other information is given below:

> X=cbind(rep(1,length(x1)),x1, x2)

> length(x)  20

> *X)

x1 x2

0.263228050 0.007856853 -0.04595048  时间序列分析代考

x1 0.007856853 1.713696862 -1.70212619

x2 -0.045950484 -1.702126187 1.69754457

>model=lm(y~x1+x2)

> anova(model)

Analysis of Variance Table

Response: y

Df Sum Sq Mean Sq F value Pr(>F)   时间序列分析代考

x1 1 320.03 320.03 217.8253 9.74e-11 ***

x2 1 2.49 2.49 1.6949 0.2114

Residuals 16 23.51 1.47

> model\$coef

(Intercept)                 x1                      x2

1.570008                 3.555795                -2.055999

>model2=lm(y~x1)

> anova(model2)

Analysis of Variance Table

Response: y

Df Sum Sq Mean Sq F value Pr(>F)

x1 1 320.03 320.03 209.27 5.494e-11 ***   时间序列分析代考

Residuals 17 26.00 1.53

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

> model3=lm(y~x2)

> anova(model3)

Analysis of Variance Table

Response: y

Df Sum Sq Mean Sq F value Pr(>F)

x2 1 315.146 315.146 173.46 2.393e-10 ***

Residuals 17 30.886 1.817

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

> cor(x1,y)  0.9617011

> cor(x2,y)  0.9543288

> cor(x1,x2)  0.9979624

(i)Find a 95% c.i. for β2. Make a decision based on your c.i. if we can acept

H0 : β2 = 0 at α = 5% level.

(ii)Check the validity of both model 2 and model 3. How do you explain your results based on the provided Routput?

(iii)Do you suggest removing x1as a predictor? Why?

### 3.Let  时间序列分析代考

where ∈i. N (0, σ2).

(i)Explainhow we can write this model as a linear regression with the regular assumptions in this course. Does the regular assumptions hold?

(ii)Findthe L.E. for β  and σ2 denoted by βˆ and σˆ2,  respectively based on the modified model.  Find the distribution for βˆ. 