# Calculate the conditional variance when there is a positive and negative shock of 0

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```					                                  Exercises

Lecture 1

1) Discuss some of the reasons for using a panel dataset rather than a time series
or cross section dataset.

2) What is unobserved heterogeneity and what is its affect on the estimators?

3) Explain how the use of fixed effects overcomes the unobserved heterogeneity.

4) Compare and contrast the three main approaches to the use of fixed effects
models.

5) Evaluate how random effects models can improve on fixed effects models,
how can we test for the most appropriate method?

6) Based on the paper on the web page: ‘Collateral damage: Effects of the
Japanese bank crisis on real activity in the United States’ by Peek and
Rosengren.

a) Discuss the data sets used in this paper and explain some of the
limitations of this data set.
b) Does the approach adopted in this study suit the model used by the
authors?
c) Critically appraise the results obtained in Table 3, what additional tests
could have been run?
d) Suggest how you might extend this study into a further piece of
research in this area.

Lecture 2

1) What criteria determine whether a time series is stationary or not?

2) What is the difference between an autocorrelation coefficient and a partial
autocorrelation coefficient?

3) Describe how you would produce a correlogram and use it to determine if a
series was stationary or not.

4) Given the following information about the time series y, use the Q-statistic and
Llung-Box statistic to determine if it is stationary or not.

12
  k2  0.12
ˆ
k 1
12    2
ˆ
 (n k k )  0.07
k 1
n  36
5) What is an AR(3) model, explain using the lag operator?

6) Given the following MA(2) model

yt  u t  1u t 1   2 u t 2

Calculate the mean and variance of yt.

Lecture 3

1) Find the characteristic equation of the following AR(2) model and determine
if it is stationary.

yt  0.8 yt 1  0.15 yt 2  u t

2) Calculate the (unconditional) variance of:

yt  1 yt 1  u t

3) Critically appraise the Box-Jenkins methodology to ARIMA modelling, to
what extent is it more art than science?

4) Assess the difference between an in-sample and an out-of-sample forecast,
which is the most useful? What is the Mean Square Error (MSE) and what are
some of its failings when assessing the accuracy of a forecast?

5) Describe how you would calculate a statistic which measures the % of correct
signs predicted, why is this so important to finance?

6) Critically appraise the use of ARIMA models as set out in the paper by Harvey
(1997) on the web page.

Lecture 4

1) What is the difference between a stationary process and a trend stationary
process? What is the difference between an I(1) and I(2) variable?

2) Explain how the Augmented Dickey-Fuller test works, what are some of the
limitations of this test?

3) What do you understand by the term ‘cointegration’, what are the implications
of regressing an I(1) variable against another I(1) variable?

4) Following a regression of income on consumption, the residuals were saved
and an ADF test was conducted giving the following result:
ut  0.7ut 1  0.3ut 1
ˆ
   (0.15)(0.12)
(Standard Error in Parentheses)

i)     Why has the lagged dependent variable been added to this regression?
ii)    Is there any evidence of cointegration between these two variables?

5) Explain what the ‘Granger Representation Theorem’ is and what its
implications for the error correction term are?

6) Given the following Error Correction Model between stock prices and money
supply:

st  0.7  0.2mt  0.6( st 1  mt 1 )
ˆ
(2.8) (2.7)        (3.2)
(asymptotic t-statistics in parentheses, 60 observations used)
Interpret the above model, with particular reference to the error correction term.

Lecture 5 + 6

1) Explain what ‘simultaneous equation bias’ is and what effect it has on the
estimates using OLS.

2) Produce a reduced form model, based on the following two equations for stock
prices (s) and investment (I).:

st   0  1 yt   2 I t  u1t
I t   0  1 s t  u 2 t
Where s and I are endogenous and y is exogenous. Which of the above models is
identified?

3) Explain how ‘Two-Stage-Least-Squares’ works and what its advantages and

4) Why is a Vector Autoregression (VAR) a means of overcoming the problem of
endogeneity?

5) Produce a VAR specification from the following three variables: et, st and it.

6) Explain how to conduct a ‘Granger causality Test’ using a VAR.
Lecture 7

1) What are some of the limitations of the ‘Granger causality’ test?

2) Evaluate the use of information criteria such as the Schwarz-Bayesian
information criteria in determining the optimal lag length to use in a VAR.

3) Trace out the time path of the impulse response function for the following first
order VAR:

f t  A1 f t 1  ut
Where :
 0. 7 0 . 3 
A1              
 0 0.9
4) Critically appraise the use of the VAR approach with financial variables.

5) What is a Vector Error Correction Model (VECM), how do these improve on
the basic VAR?

6) What is the difference between long and short run causality?

Lecture 8

1) Why is the Engle-Granger two stage approach to cointegration less appropriate
when there are more than two endogenous variables in the model?

2) What is the difference between the α coefficients and the β coefficients with
respect to the π matrix in the Johansen Maximum Likelihood procedure?

3) Given the following results from a Johansen Maximum Likelihood test, how
many cointegrating vectors are present:

Trace Test Results
Null  Alternative                   Trace       Critical value
5% value

r  0, r  1           27.3                          23.8
r  1, r  2           14.5                          12.0
r  2, r  3            2.7                           4.2
Maximum Eigenvalue Results
Null Alternative       Max                      Critical value
5% value

r  0, r  1                      25.7                  20.2
r  1, r  2                      12.4                  12.7
r  2, r  3                       2.7                   4.2
4) What is the main difference between the trace test and maximum Eigenvalue
test when conducting the Johansen ML procedure

5) What is a Vector Error Correction Model and why is it related to the Johansen
Maximum Likelihood procedure?

6) Critically Appraise the use of the Johansen ML procedure, with particular
reference to the Wickens critique.

Lecture 9

1) Discuss the theoretical reasons for using a dynamic panel.

2) What is the main difference between the Arellano-Bond and Arellano-Bovver
approaches to dynamic panels?

3) Outline the main steps involved in carrying out a dynamic panel model
estimation and critically appraise the dynamic panel approach..

4) Explain the two main methods for carrying out a panel unit root test.

5) Discuss the main problems with the Levin Lin and Im Pesaran and Shin
approaches to testing for a unit root.

6) Briefly examine the panel approach to cointegration.

Lecture 10

1) What is the main difference between the Maximum Likelihood method and
the Least Squares approach?

2) What is the leverage effect? Why is it a particular problem for financial data?

3) Explain what an autoregressive conditional heteroskedastistic effect is and
why is this form of modelling important for financial data?

4) Explain the specification of the following model:

 t2   0  1ut2  1 t21   2 t22

What is the non-negativity constraint with respect to the above equation?

5) Why is a GARCH(1,1) model a more parsimonious version of the ARCH
model which includes a large number of lags?

6) Show that the GARCH model can be expressed as an ARMA model for the
fitted variance.
Lecture 11

1) Why is it important to incorporate asymmetric adjustment into GARCH style
models?

2) Explain how this asymmetric adjustment is incorporated into the Glosten,
Jagannathan and Runkle model (GJR).

3) How does the non-negativity constraint change in the GJR model?

4) Given the following result:

yt  0.7
 (0.2)
 t2  0.92  0.15ut21  0.36 t21  0.27ut21 I t 1
 (0.45)  (0.07)  (0.12)  (0.10)
whereI t 1  1 : ut 1  0
     0otherwise
(Standard errors in parentheses)

a. Does the above model suffer from asymmetric adjustment?
b. Calculate the conditional variance when there is a positive and
negative shock of 0.2 and    t21  0.76 .

5) Explain how the GARCH-in-mean model works, with particular reference to
measuring risk and return in an asset.

6) What are the main uses of the GARCH type of models?

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 views: 5 posted: 10/1/2012 language: English pages: 6