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FORMAL EXAMINATION PERIOD: SESSION 1, JUNE 2016

Econ334

Financial Econometrics

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

Question 1.

Which of the following sets of characteristics would usually best describe an autoregressive process of order 2 (i.e. an AR(2))?

(a) A slowly decaying ACF, and a PACF with 2 significant spikes

(b) A slowly decaying PACF and an ACF with 2 significant spikes

(d) An ACF and a PACF with 3 significant spikes

(e) None of the above

Question 2.

Suppose a series yt follows the process

yt = yt 1 + ct

where ct is a white noise process. What is the optimal 1‐step ahead forecast of yt ?

(a) The current value of y (i.e. yt )

(b) Zero

(d) A geometrically declining weighted average of past values of y

(e) One

Question 3.

Consider a series that follows an MA(1) with zero unconditional mean and a moving average coefficient of 0.4. What is the value of the autocorrelation function at lag 1?

(a) 0.4

(b) 1

(d) 0.16

(e) It is not possible to determine the value of the autocovariances without

knowing the disturbance variance.

Question 4.

Suppose that you have estimated the first five autocorrelation coefficients using a series of length 81 observations and found them to be

Lag	1	2	3	4	5
Autocorrelation Coefficient	0.412	‐0.205	‐0.332	0.005	0.543

Which autocorrelation coefficients are significantly different from zero at the 5% level?

(a) The first and fifth autocorrelation coefficient

(b) The first, second, third and fifth autocorrelation coefficient

(d) The second and fourth autocorrelation coefficient

(e) The fourth autocorrelation coefficient

Question 5.

Is the following process yt = 3yt 一1 一 2yt 一2 + ut stationary?

(a) It is stationary

(b) It is not stationary

(d) It is only partly not stationary

(e) None of the above

Question 6.

What is an appropriate approach to testing for ‘ARCH effects’?

(a) Run a regression, collect the residuals, regress the squared residuals on their

lags and conduct a hypothesis test to check whether the coefficients of the lagged squared residuals are equal to zero

(b) Run a regression, collect the fitted values, regress the fitted values on their

squared lags and conduct a hypothesis test to check whether the coefficients of the lagged squared fitted values are equal to zero

(c) Run a regression, collect the residuals, regress the residuals on their lags and conduct a hypothesis test to check whether the coefficients of the lagged residuals are equal to zero

(d) Run a regression, collect the fitted values, regress the fitted values on their lags and conduct a hypothesis test to check whether the coefficients of the lagged fitted values are equal to zero

(e) None of the above

Question 7.

Suppose the process for yt is given by

yt = 2.0 + 0.8yt一1 + ut

where ut is white noise. Then the optimal forecast of yt+j as j becomes very large (i.e. as j ) is

(d) 2.0

(b) 0.0

(d) Infinity (i.e. )

(e) None of the above

Question 8.

What are the steps required to estimate an ARCH/GARCH model?

(a) First specify the appropriate equations for the correlation and the variance,

then specify the Log‐ Likelihood Function (LLF) and the computer will generate parameter values that maximise the LLF

(b) First specify the appropriate equations for the correlation and the variance,

then specify the Log‐ Likelihood Function (LLF) and the computer will generate parameter values that minimise the LLF

(c) First specify the appropriate equations for the mean and the variance, then specify the Log‐ Likelihood Function (LLF) and the computer will generate parameter values that maximise the LLF

(d) First specify the appropriate equations for the mean and the variance, then specify the Log‐ Likelihood Function (LLF) and the computer will generate parameter values that minimise the LLF

(e) None of the above

Question 9.

GJR and EGARCH are types of GARCH models that allow for:

(a) An asymmetric response of returns to positive and negative shocks in the dependent variable

(b) An asymmetric response of returns to positive and negative shocks to its lagged values

(d) An asymmetric response of volatility to positive and negative shocks

(e) None of the above

Question 10.

The news impact curve is

(a) A function of lagged news shocks

(b) A function of squared news shocks

(d) A function of lagged squared news shocks

(e) None of the above

Question 11.

Consider the following bivariate VAR(2):

y1t = 10 + 11y1t 1 + 12y1t 2 + 13y2t 1 + 14y2t 2 + u1t

y2t = 20 + 21y1t 1 + 22y1t 2 + 23y2t 1 + 24y2t 2 + u2t

Which of the following coefficient significances are required to be able to say that y1 Granger‐causes y2 but not the other way around?

(a) 13 and 14 significant; 21 and 22 not significant

(b) 21 and 22 significant; 13 and 14 not significant

(d) 11 and 13 significant; 21 and 23 not significant

(e) None of the above

Question 12.

A researcher would like to run an augmented Dickey‐ Fuller test on the variable yt . What is the regression that would be estimated and what is the null hypothesis (H0 ) of the test?

(a) yt = yt 1 + pi yt i + ut and H0 : = 0 , respectively

i=1

(e) yt = yt 1 + pi yt i + ut and H0 : 0 , respectively

Question 13.

Two variables are said to be cointegrated if

(a) If the two variables are I(0) and a linear a combination of the two are I(1)

(b) If the two variables are I(1) and a linear a combination of the two are I(1)

(d) If the two variables are I(1) and a linear a combination of the two are I(0)

(e) If one variable is I(1), the other is I(0) and a linear combination of the two are I(0)

Question 14.

Which constraints must be imposed on Gt2 = c + au1 + bG1 to produce valid estimates of volatility

(b) c > 0

(b) a > 0, b > 0

(d) a > 0, b > 0, a + b < 1

(e) None of the above

Question 15.

Volatility clustering means the following

(a) Large absolute returns tend to be followed by more large absolute returns,

small absolute returns tend to be followed by more small absolute returns.

(b) Large negative returns tend to be followed by more large negative returns,

small negative returns tend to be followed by more small negative returns

(c) Large absolute returns tend to be followed by small absolute returns, small absolute returns tend to be followed by large absolute returns.

(d) Large positive returns tend to be followed by more large positive returns, small positive returns tend to be followed by more small positive returns

(e) None of the above

Question 16.

Which of the following conditions must hold for an ARMA model to be invertible?

(a) All roots of the AR characteristic equation must lie outside the unit circle

(b) All roots of the MA characteristic equation must lie outside the unit circle

(d) All roots of the MA characteristic equation must lie inside the unit circle

(e) None of the above

Question 17.

The Engle and Granger approach to testing for cointegration is a test for non‐ stationarity in

(a) The dependent variable in the Engle‐Granger regression

The independent variables in the Engle‐Granger regression

The fitted values from the Engle‐Granger regression

(d) The residuals from the Engle‐Granger regression

(e) None of the above

Question 18.

Given the following forecasts and actual values of a return series what is the percentage of correct sign predictions?

Forecast

Actual

‐0.20

0.15

‐0.20

0.06

‐0.04

‐0.40

0.20

0.10

‐0.10

0.05

(a) 10%

(b) 20%

(d) 40%

(e) 60%

Question 19.

Suppose that a researcher wishes to test for calendar (seasonal) effects using a dummy variables approach. Which of the following regressions could be used to examine this?

(i) A regression containing intercept dummies

(ii) A regression containing slope dummies

(iii) A regression containing intercept and slope dummies

(iv) A regression containing a dummy variable taking the value 1 for one

observation and zero for all others

Your answer is regressions:

(a) (ii) and (iv) only

(b) (i) and (iii) only

(d) (i), (ii), (iii), and (iv).

Question 20.

Consider the series shown in the following graph.

The plotted series in the above graph is an example of a:

(a) Stationary process

(b) Deterministic trend process

(d) Random walk with drift

Part B – There are FOUR questions, and each question has parts to it. Each question is worth 5 marks in total. Answer ALL FOUR questions (for 20 marks in total) in the examination booklet provided.

Question 1.

You have estimated the following ARMA(1,1) model for some time series data yt = 0.05 + 0.75yt 一1 + 0.25ut 一1 + ut

Suppose you have data for time to t, i.e. you know that yt = 3.4, and ut =一1.5 .

(a) Obtain the forecast for the series y for times t+1 and t+2 using the estimated

ARMA model.

(b) If the actual values for the series y turned out to be ‐0.05 and 0.95 for t+1 and

t+2, respectively, calculate the out‐of‐sample mean squared error.

(c) What value does the long run forecast for y converge to? (i.e. What is forecast value of yt +j as j becomes very large i.e. as j ?).

Question 2.

A researcher has data on the daily percentage return on the AUD/US exchange rate from 5 January 1999 to 30 September 2004, a total of 1,442 observations. The return series, which is denoted REX, is shown in the graph.

- 1

-2

-3

-4

REX

250 500 750 1000 1250

A Dickey‐ Fuller test using EViews was performed on the series. The results are shown below.

-Statistic Prob.*

DF test statistic -39.7544 0.0000

Test critical values: 1% level -3.43468

5% level -2.86334

10% level -2.56778

*MacKinnon (1996) one-sided p-values.

(a) What do you conclude?

(b) The researcher regressed REX on a constant and, using the estimated

residuals, performed an LM test for seventh‐order ARCH effects by way of an auxiliary regression. It gave an R2 of 0.017. Construct an LM test for ARCH effects and interpret your result. In your answer be sure to specify the null and alternative hypotheses and the auxiliary regression. (Note that

t0.05,7 = 1.90 and X0(2)05,7 = 14.07 ).

The researcher decided to estimate a GARCH(1,1) model for the conditional volatility of REX. (For the mean equation, REX is simply regressed on a constant. For the variance equation, a GARCH(1,1) is specified). The results from EViews are shown below.

Dependent Variable: REX