QUESTION 1 (40 Marks)

Below is a regression output from R. Answer the following questions based on the regression output and assuming a significance level = 0.05

>lm  msoft         =lm(er  msoft         ～er  sandp+r  term         +d  money+d  inflation,data         =         macro  1)

>     summary(lm  msoft)

lm(formula    =   er  msoft    ～er  sandp+r  term    +   d  money    +d  inflation,

data  =  macro  1)

Residuals :

Min          1Q Median         3Q       Max

-36.302 -4.328 -0.292   4.350 25.012

signif.codes:e“ …              8.801     8.81  ’8.85‘. ’8.1‘’1

Residual  standard  error:7.739  on  378  degrees  of  freedom

Multiple    R-squared:    0.3425,  Adjusted    R-squared:    0.3355

F-statistic:49.23   on   4   and   378   DF,   p-value:<2.2e- 16

>library(car)

>linearHypothesis(1m  msoft,c("d  money=8","d  inflation=e"))

Linear   hypothesis   test

Hypothesis:

Q5??

Model  2:er  msoft  ～er  sandp+  r  term  +  d  money  +  d  inflation

Res.Df          RsS   Df    Sum  of    Sq     F Pr(>F)

1      380.22850           

2   Q6?           264d    Q6?      ]09.961.7528      θ.1747

1.1 What is the dependent variable? What are the independent variables? (5 Marks) 1.2 Interpret the regression result with regards variable r_term. (5 Marks)

1.3 Calculate the t-value of the term d_money. (5 Marks)

1.4 What are the null hypothesis and alternative hypothesis of t-test with regards variable d_inflation? (5 Marks)

1.5 What are the null hypothesis and alternative hypothesis at the blank “Q5” in the output? (5 Marks)

1.6 Calculate the d.f. of the F-test (5 Marks)

1.7 Consider we want to find the final model by backward variable screening method. What is the model we should start with? (5 Marks)

1.8 Why do we always want to include an error term in a regression model? (5 Marks)

QUESTION 2 (40 Marks)

Consider the following ARMA(2,1) process:

yt  = 2 − 0.3yt−1  + 0. 1yt−2  + 0 5u.t−1

Where ut ~ N(0,  2 )

2.1 Is yt  stationary? Explain your answer by mathematical proof.   (20 Marks)

2.2 Describe what the ACF and PACF look like for the process, respectively. (You do not need to calculate both functions, simply consider what shape it might give). (10 Marks)

2.3 Given ut−1  = 0.3, yt−1  = −0.6, yt−2  = 0.4, Calculate the two-step forecast if all information until t– 1 is available (i.e., E(yt+1|t−1)). (10 Marks)

QUESTION 3 (20 Marks)

3.1 Comparing to adjusted R2 , what is the disadvantage of R2 ? Why we need to introduce adjusted R2 ? (10 Marks)

3.2 Briefly explain pitfalls of regression model.  (10 Marks)