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Multiple Choice Test Bank Questions No Feedback – Chapter 9
Correct answers denoted by an asterisk.
1. Volatility clustering is
2. Which of the following is true about ARCH and GARCH models?
(I) They are used for modelling and forecasting volatility
(II) They are non-linear models
(III) They can both be estimated using OLS
(IV) Series estimated using these models must have a unit root process
3. Which of these cannot be used to test for non-linearity?
4. Which of the following statements are true regarding volatility:
(I) It measures the total risk of financial assets
(II) It can be used in computing value-at-risk
(III) It is a component of the Black-Scholes formula for deriving the prices of traded
options
(IV) It can be estimated using the variance of asset returns
5. What are the names of the following models?
(I)
22
0 1 1tt
u
−
=+
(II)
2 2 2
0 1 1 1t t t
u
−−
= + +
(III)
2 2 2 2
0 1 1 2 2 ...
t t t q t q
u u u
− − −
= + + + +
(IV)
2 2 2 2 2 2 2
0 1 1 2 2 1 1 2 2
... ...
t t t p t p t t q t q
u u u
− − − − − −
= + + + + + + + +
6. What is an appropriate approach to testing for ‘ARCH effects’?
7. Which of these is an appropriate technique used in estimating models from the
GARCH family?
8. What are the steps required to estimate an ARCH/GARCH model?
9. GJR and EGARCH are types of GARCH models that allow for:
10. Assume that you have estimated a GJR model of monthly stock returns and you
obtain the following equations:
0.125
t
y=
2 2 2 2
1 1 1 1
1.102 0.115 0.641 0.175
t t t t t
u u I
− − − −
= + + +
Suppose that
210.721
t
−=
, what would be the fitted conditional variance for time t if
1
ˆ0.5
t
u−=
and then if
1
ˆ0.5
t
u−=−
?
11. Suppose that a researcher estimates a GARCH(1,1) model and obtains a log
likelihood function (LLF) value of 71.22. He is interested in testing whether an ARCH(1)
model is a better model at describing volatility. If he estimates a model which imposes
the necessary restrictions and obtains an LLF value of 68.21, what would be the
1. What would typically be the shape of the news impact curve for a series that exactly
followed a GARCH(1,1) process?
12. Which of the following are NOT features of an IGARCH(1,1) model?
(i) Forecasts of the conditional variance will converge upon the unconditional variance as
the horizon tends to infinity
(ii) The sum of the coefficients on the lagged squared error and the lagged conditional
variance will be unity
(iii) Forecasts of the conditional variance will decline gradually towards zero as the
horizon tends to infinity
(iv) Such models are never observed in reality
13. Which of the following would represent the most appropriate definition for implied
volatility?
14. Suppose that a researcher wanted to obtain an estimate of realised (“actual”)
volatility. Which one of the following is likely to be the most accurate measure of
15. Which of the following is the most plausible test regression for determining whether a
16. Consider the following conditional variance equation for a GJR model.
ht =
0 +
1
21−t
u
+
ht-1+
ut-12It-1
where It-1 = 1 if ut-1 < 0
= 0 otherwise
For there to be evidence of a leverage effect, which one of the following conditions must
hold?
17. Consider the three approaches to conducting hypothesis tests under the maximum
likelihood framework. Which of the following statements are true?
(i) The Wald test is based on estimation only under the null hypothesis
(ii) The likelihood ratio test is based on estimation under both the null and the
alternative hypotheses
(iii) The lagrange multiplier test is based on estimation under the alternative
hypothesis only
(iv) The usual t and F-tests are examples of Wald tests
18. Which one of the following problems in finance could not be usefully addressed by
either a univariate or a multivariate GARCH model?
