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FORMAL EXAMINATION PERIOD: SESSION 1, JUNE 2019

ECON334

Financial Econometrics

Part A – Multiple Choice Questions (20 in total, 1 mark each)

Question 1

Consider the following process:

yt = 0.5 + 0.2ut−3 + 0.3ut−2  + 0.4ut−1 + ut

What is the optimal forecast of yt+2 , given that all information up to and including time t is available; in particular that ut = 0.4, ut−1  = 0.6, ut−2  = 0.5 and ut−3  = −0.2.

(a)   4.9

(b)   2.9

(c)   1.3

(d)   0.5

(e)   None of the above

Question 2

The random variable yt follows the ARMA(1,2) process given by:

yt = 3.0 + 0.4yt−1 + 0.7ut−2  − 0.4ut−1 + ut where ut is a white noise process. The unconditional mean of yt is:

(a)       5.0

(b)       0.0

(c)        3.0

(d)        1.8

(e)        None of the above

Question 3

An invertible moving-average process of order two (i.e. an MA(2)) would have the following characteristics:

(a)       a decaying ACF and PACF

(b)        an ACF and a PACF with two significant spikes

(c)        an ACF with one significant spike and an PACF with two significant spikes

(d)        a decaying PACF, and an ACF with two significant spikes

(e)       a decaying ACF, and a PACF with two significant spikes

Question 4

Which of the following statements are likely to be true in relation to the behaviour of daily returns from shares traded on a major stock exchange?

(i) returns cannot usually be forecast with any accuracy because the time series of stock prices resembles a random walk

(ii) ARCH and GARCH can be useful for modelling common patterns in the variance of returns such as volatility clustering

(iii) share prices usually fluctuate around a deterministic time trend

(iv) there is no pattern in either share returns or in the variance of returns.

(a)       (i) only

(b)       (iii) only

(c)         (i) and (ii) only

(d)       (iii) and (iv) only

(e)       (i) and (ii) and (iii) only

Question 5

Consider an AR(1) – GARCH(1,1) model of returns, given by:

yt = c + φyt−1 + ut

σt2  = α0  + α1u1 + βσt1

What are the conditions that need to be satisfied to ensure that u has a well-defined

conditional and unconditional variance?

(b) φ+α1 + β< 1

(c) α1 + β< 1

(d)       Conditions (a) and (b)

(e)       Conditions (a) and (c)

Question 7

What condition on the parameters will make the conditional variance more responsive to negative ‘news’ shocks than to positive ‘news’ shocks in the EGARCH model below?

log(σt(2)) = ω + α | ut−1 | + βlog(σ1 ) +γ ut−1

σt−1 σt−1

(b) α > 0

(c) α < 0

(d) γ > 0

(e) γ < 0

Question 8

Consider the following bivariate VAR(2):

y1t = α10 + α11y1t−1 + α12y1t−2 + α13y2t−1 + α14y2t−2 + u1t

y2t = α20 + α21y1t−1 + α22y1t−2 + α23y2t−1 + α24y2t−2 + u2t

When y1    does not Granger-cause y2   but y2  does Granger-cause y1 , it is the case that:

(a) α21  and α22   not significant; α13  and α14  significant

(b) α21  and α22   significant; α13  and α14   not significant

(c) α21  and α23   significant; α11  and α13   not significant

(d) α21  and α23 not significant; α11  and α13  significant

(e)        None of the above

Question 12

Consider the process yt = 3yt−1 − 2yt−2 + ut , where ut is white noise. Consider the following statements about the stationarity of yt :

(i)        the relevant characteristic polynomial is 1 − 3z + 2z2 with roots equal to 1.0 and 0.5

(ii)        the relevant characteristic polynomial is 1 + 3z − 2z2   with roots equal to 0.5 and 2

(iii)       the relevant characteristic polynomial is z2  − 3z + 2 with roots equal to 1.0 and 2

(iv) yt is a stationary process

(v) yt is a non-stationary process

Which of the above statements are true concerning the stationarity of yt ?

(a)       (iii) and (v) only

(b)       (ii) and (iv) only

(c)       (iii) and (iv) only

(d)       (i) and (iv) only

(e)       (i) and (v) only

Question 13

The data generating model for first differences of yt is given as follows:

∆yt = c + ∆yt−1 + ut

where ut is a white noise process and c is a constant term.

Which statement is correct?

(a) yt is an I(0) process

(b) yt is an I(1) process

(c) yt is an I(2) process

(d)        ∆yt is an I(2) process

(e)        ∆yt is an I(0) process

Question 17

Consider the following statements about ARCH and GARCH models:

(i)          They are used to model the conditional variance of a time series

(ii)         They model volatility clustering in the data

(iii)        They are applied to non-stationary time series

(iv)        The conditional variance is time varying but the unconditional variance is constant and generally finite

Which of those statements is correct:

(a)       (ii) only

(b)       (i) and (ii) only

(c)        (i), (ii) and (iii) only

(d)        (i), (ii) and (iv) only

(e)       All of the statements are correct

Question 18

A researcher is trying to select an appropriate ARMA model for a data series. Three different models are considered: ARMA(1,2), AR(2) and MA(2). Each model was estimated with an    intercept term using 50 observations. The log of the estimated residual variance i.e. ln(σˆ 2 )   for each model is shown in the table below. Which model would be selected based on the     AIC information criteria?

Model	ln(σˆ 2 )
ARMA(1,2)	0.91
AR(2)	0.97
MA(2)	0.92

(a)       ARMA(1,2)

(b)       AR(2)

(c)         MA(2)

(d)       There is not enough information to calculate the AIC value for each model (e)       The AIC value is the same for each model so any can be selected

Question 19

Suppose the process for yt is given by

yt = 0.6 + 0.4yt−1 − 0.5ut−1 + ut

where ut is white noise. Compute the expectation of yt+1 , conditional on the information available at time t −1,  namely, that yt−1  = 0.5 and ut−1  = 0.6. The answer is:

0.4

(b)

(c)

(d)

(e)