1. (40 Marks)

1.1 Er_msoft is the dependent variable. Er_sandp, r_term, d_money, d_inflation are

independent variables. (5 Marks)

1.2 Since significance level = 0.05 (beginning of this question), p-value of t-test of r_term is 0.00534 which is smaller than 0.05, so the coefficient of r_term is significant. Therefore, r_term can significantly influence er_msoft. When r_term increases by 1 unit, the

expected value of er_msoft increases by 4.738066 unit.  (5 Marks)

1.3 T-value = -0.006431 / 0.014972 = -0.4295 (5 Marks)

1.4 Null hypothesis: the coefficient of d_inflation is zero.

Alternative hypothesis: the coefficient of d_inflation is NOT zero. (5 Marks)

1.5 Null hypothesis: Coefficients of BOTH d_money and d_inflation are zero.

Alternative hypothesis: NOT BOTH coefficients are zero. (5 Marks)

1.6 D.f. of F-test = 2, 378 (5 Marks)

1.7 For the backward variable screening method, we should start with the full model, which is the model includes all independent variables.  (5 Marks)

1.8 1) We always leave out some determinants of Y.

2) There may be errors in the measurement of Y that cannot be modelled.

3) Random outside influences on Y which we cannot model. (From P8 LT4) (5 Marks)

2. (40 Marks) 2.1

The model can be written as:  yt  + 0.3 Lyt  − 0. 1 L2yt  = 2 + 0 5u.t−1

So, the characteristic equation: 1 + 0.3L − 0. 1L2  = 0

The characteristic roots (solution of the equation): L = −2, 5

Since the absolute values of both roots are larger than 1, the process yt  is stationary. (20 Marks)

2.2 Since it is a ARMA process, both ACF and PACF decay geometrically. (10 Marks)

2.3 One-step forecast: E(yt |yt−1) = 2 − 0.3 ∗ (−0.6) + 0. 1 ∗ 0.4 + 0.5 ∗ 0.3 = 2.37

Two-step forecast: E(yt+1|yt−1) = 2 − 0.3 ∗ 2.37 + 0. 1 ∗ (−0.6) + 0.5 ∗ 0 = 1.229 (10 Marks)

3. (20 Marks)

3.1 1) R2  never decrease if more regressors are added to the regression.

2) R2  does not consider the loss of degrees of freedom when adding extra variables. (From P17-16 LT5) (10 Marks)