Question 3 [25 marks]
You estimate the model
_ = + 1 + 2 _ + ,
using quarterly data. Results are reported in Table 1.
Table 1: OLS estimates using 174 observations
Dependent variable: Interest rate

Variable

Coefficient

Std. Error

tStatistic

Prob.
















CONSTANT

0.045836

0.113503

0.403833

0.6869


INFLATION

0.204347

0.020596

9.921921

0.0000


OUTPUT GAP

0.022601

0.063539

0.355710

0.7225












Rsquared

?

Mean dependent var

0.753494


Adjusted Rsquared

?

S.D. dependent var

1.415286


S.E. of regression

1.114094

Akaike info criterion

3.072648


Sum squared resid

193.6281

Schwarz criterion

3.130552


Log likelihood

241.2755

HannanQuinn criter.

3.096162


Fstatistic

49.48873

DurbinWatson stat

0.051860


Prob(Fstatistic)

0.000000



















a)Are 1 and 2 statistically significant? Explain.
b)Calculate 2 and adjusted 2 using the results reported in Table 1. Discuss the two statistics and the results obtained.
Question 4 [25 marks]
a)Consider the following autocorrelation and partial autocorrelation coefficients estimated using 500 observations from a weakly stationary stochastic process :
Lag

ACF

PACF







1

0.307

0.307

2

0.013

0.264

3

0.086

0.147

4

0.031

0.086

5

0.019

0.049







3
Which of the autocorrelations are statistically significantly different from 0? Also, using both the BoxPierce and the LjungBox test statistics, test the null hypothesis that the first five autocorrelations are all jointly equal to 0.
b)What process would you tentatively suggest could represent the most appropriate model for the series whose ACF and PACF are presented in part (a)? Explain your answer.
c)Two researchers are asked to estimate an ARMA model for a daily USD/GBP exchange rate return series,denoted . Researcher uses the Bayesian Information Criterion for determining the appropriate model and arrives at an
ARMA(0,1). Research uses Akaike’s Information Criterion which deems an
ARMA(2,0) to be optimal. The estimated models are
: ̂ = 0.38 + 0.10−1
: ̂ = 0.63 + 0.17−1 − 0.09−2
where is a White noiseprocess.
You are given the following data:
= 0.31,

−1 = 0.02,

−2 = −0.16



−1

= 0.13,


−2

= 0.19

Produce forecasts for=the−0.02,next



from both models.

4 days, i.e., for times + 1, + 2, + 3, and + 4,

d)How could you determine whether the models proposed in part (c) are adequate?
e)Suppose that the actual values of the series on days + 1, + 2, + 3, and + 4turned out to be 0.62, 0.19, −0.32, and 0.72, respectively. Determine which researcher’s model produced the most accurate forecasts.