Shuailin Li doc. Student No. 0922994

Quantitative Method Project BST164

NAME: SHUAILIN LI

STUDENT NO.:0922994

DATE: 11TH FEB 2013

1

Question 1

As can be seen from the following

table, the dependent variable is well

explained by the independent

variables since the R-Squared is

relative high and it is very close to

one.Additionally, the p-value of both

independent variables is equal to zero

which

means they are both significant in this equation. (I)

DW test

H 0: ρ=0

H 1: ρ>0 or ρ<0.

Referring to the DW tables with k=2 and n=55 for the 5% significance level, we see that d L =1.49. Since d

(II)

Breusch-Godfrey LM test

H 0: e t ~ N (0, σ2 I)

H 1: e t is generated by AR (p)

e t is generated by MA (p) process.

The null hypothesis of no serial correlation is strongly rejected.

(III)

Box-Pierce test

H 0: ρ1=ρ2=…=0

H 1: ρ1≠ρ2≠ 0

Reject the null hypothesis of autocorrelation

coefficients are zero.

(IV)

Breush-Pagan test

H 0:there is NO heteroscedasticity

H 1: there is heteroscedasticity.

We can reject the null hypothesis of no heteroscedasticity.

2

(V)

RESET testis

H 0: the linear functional form is correct

H 1: the functional form is of higher order.

Reject the null hypothesis of the linear

functional form is correct.

(IV)

Chow test

H 0: there is NO structural break

H 1: there is structural break

Reject the null hypothesis.

(1.2)

Wald test

H 0: β=1

H 1: β≠1.

The null hypothesis should clearly be rejected

Question 2

We can see from the table that the p-

value of constant and the inflation are

both larger than 0.05, which means these

two variables are not significant in this

equation. On the other hand, LNK and

FD have less standard deviation and zero

probability. These two estimations

illustrate that they are significant while R-squared is also close to 1 meaning the dependent variables can be explained well by the independent variables.

(I)

DW-statistics is 0.251243 which is smaller than 2, so there is positive first order serial correlation of the error term.It is also smaller than the critical value, thus reject the

null of non-autocorrelated

3

(II)

TheBreusch-Godfrey LM test H 0:e t ~ N (0, σ2 I) H 1: e t is generated by AR (p) process

e t is generated by MA (p) process TR 2=42.27822>χ2 (0.95, 2) =5.991 so the null hypothesis o

f no serial correlation is strongly rejected. (III)

Box-Pierce statistics H 0: ρ1 = ρ2 = …= 0 H 1: ρ1 ≠ρ2 ≠…≠ 0 Since Q*=99.530>χ0.952(4)=9.488, Reject

the null hypothesis of autocorrelation coefficients are zero. (IV)

Breusch-Pagan test H 0: There is NO heteroscedasticity H 1: There is heteroscedasticity. Reject the null hypothesis. (V)

RESET test

H 0: the linear functional form is correct H 1: the functional form is of higher order. Reject the null hypothesis. (VI)

Chow test

H 0: there is NO structural break H 1: there is structural break Reject the null hypothesis. Wald test

H 0: θ2=θ3=0

H 1: θ2≠θ3≠0

Null hypothesis is rejected

4

(2.1)

The table on the left shows the weighted least square using inflation as the weight. As we can see there are some differences between the weighted statistics and the unweighted statistics. As a result of R 2 is bigger in weighted model than in unweighted model, the dependent variable in weighted model is explained better than in OLS. Moreover, the mean of dependent

variable in weighted statistics is less than the unweighted one but the S.D. in WLS is much higher than that in OLS. However, the inflation is still not very relevant and significant in both WLS and OLS since the p-value is bigger than 0.05 (2.2)

Hausman ’s test of endogeneity H 0: lnk is exogenous H 1: lnk is endogenous

Reject the null hypothesis. So lnk is endogenous. (2.3)

In

TSLS,

the

coefficients

of

independent variable have changed a lot but the significance of them has not changed.

(2.4)

Sargan ’s instrument validity test H 0: instruments (r, lnpop, infd and infl) are valid

H 1: instruments (r, lnpop, infd and infl) are not valid.

The test statistics is

SARG=(54-

5

4)*0.039563=1.97815 comparing with chi-square critical value χ0.952(4)=9.488, so we cannot reject H 0 and the conclusion is the instruments are valid. Question 3

(I)

From the table we can see that the

dummy variable is highly significant

and has the least S.D. By comparing

the results with the regression that

excluded the dummy variables, it can

be seen that the coefficient estimates

on the remaining variables change

quite a bit. Then the intercept has

changed during the period of 2000-

2011.

(II)

When a slope dummy variable is

included in the estimate equation, it

can be seen that the dummy

variable is not significant because

the p-value is bigger than the

critical value of t-statistic.However,

the R-square does not change very

much. Slope coefficient has not

changed during the period of 2000-2011

(III)

The intercept and slope dummy

variables in this equation are also not

significant because of the p-value is

larger than the significance level.

However, the coefficients of other

variables and the R-square have not

changed very much. So both intercept

and slope coefficient have not changed during the period of 1995-2000

6

Question 4 (I)

According to these tables and graphs to compare with chi-square critical value with df=4 is 9.488 and the p-value, we can conclude that for FTSE return does not have ARCH effect (2.74<9.488) while for the RPI return do have ARCH effect (24.57>9.488). (II)

As the table shows that there is GARCH effect of FTSE return but no GARCH effect of RPI.We can make this summary by comparing the p-value to the significance level and t-statistic to critical value.

RET_FTSE

RET_RPI

7

(III)

As the table shows there is evidence of asymmetric effects of ‘good news ’and‘bad news ’ on conditional volatility of stock returns in both FTSE return and RPI. (IV)

Comparing this result to the question (II), it can be seen that in terms of FTSE return the lag and GARCH variables have changed very significantly in GARCH-M than GARCH. However, these variables do not change very much between GARCH-M and GARCH in RPI.

(V)

There is IGARCH effect in both FTSE and RPI return because of the p-value is smaller than the significance level.

8

Question 5

(I)

Unit root test of LNY

H 0: lny has a unit root

H 1: trend stationary process We cannot reject the null.

H 0: lny has a unit root

H 1: level stationary process We cannot reject the null

H 0: lny has a unit root

H 1: stationary mean zero process We cannot reject the null.

H 0: lny has s unit root

H 1: level stationary process

We reject the null and 1st difference of lny is level stationary. Lny is I(1) process

Unit root test of LNK

H 0: lnk has a unit root

H 1: trend stationary process We cannot reject the null

H 0: lnk has a unit root

H 1: level stationary process We cannot reject the null.

H 0: lnk has a unit root

H 1: stationary mean zero process

We cannot reject the null.

9

H 0: lnk has a unit root

H 1: level stationary process

We cannot reject the null.

H 0: lnk has a unit root

H 1: level stationary process

We can reject the null and 2rd

difference

of lnk is level stationary, thus lnk is I(2) process

Unit root test of INFL

H 0: infl has a unit root

H 1: trend stationary process

We cannot reject the null

H 0: infl has a unit root

H 1: level stationary process

We cannot reject the null.

H 0: infl has a unit root

H 1: stationary mean zero process

We cannot reject the null.

H 0: infl has a unit root

H 1: level stationary process

Wecan reject the null so 1st

difference of

infl is level stationary. Then infl is I(1). (II)

Since lny(1), lnk(2), lnfl(1), they have different orders of integrations.So we cannot use E-G to test cointegration.lny=F(c, lnk, infl, d2lnk(-1 to -2), d2lnk(1 to 2), dinfl(-1 to -2), dinfl(1 to 2)).

There is an autocorrelation so

we

10

have to use DGLS

method. So from the

table on the right, when

we add up AR(1), there

is no autocorrelation.

Then we can reject the

null so lnylnk and infl is cointegrated

(III)

As a result of the analysis above, we can see that inflation and per capita physical capital stock affect the per capita real income while per capita real income affects itself in the following period.

(IV)

We can see from the statistics that the null hypothesis is rejected so theinfl and lnkp is conitegrated

Then we can use the granger causality

H 0: lnk does not Granger cause infl

H 1: lnk Granger cause infl

We can reject the null

H 0: infl does not Granger cause lnk

H 1: infl Granger cause lnk

We can reject the null

(V)

Because of the inflation does not Granger causes real income of the economy so there

is no need to focus on inflation controlling policies.

本文来源：https://www.bwwdw.com/article/ddze.html