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ECON3371 Financial Econometrics
Creation date：2024-05-04 15:49:33
Belonging category：经济Economics
Financial Econometrics

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ECON3371

Financial Econometrics


SUMMATIVE ASSIGNMENT

PART A: Simultaneous equations and 2SLS regression
In this part of the assignment, you will examine the relationship between stock market
returns and inflation.
1. Provide an explanation from the literature for why the relationship between stock
market returns and inflation can be simultaneous.
[5 marks]

Complete the exercises below by downloading ‘summ_assig_data_A.xlsx’ file. It
contains data on 10 variables: sp_500, cpi, aaa10y, baa10y, tb3ms, tb10y, con_credit,
ind_prod, usd_index and m1_money. The data are monthly and cover a 20-year period
from August 2001 until July 2021 inclusive. The definitions of the variables are
provided in the worksheet ‘description’ in the same .xlsx file.

Upload the above-mentioned datafile into Eviews and construct all the variables
defined in the box below (you will need these later to estimate equations 1 and 2).
• Stock market returns = ln (
sp_500
sp_500−1
) ∗ 100
• Inflation rate = ln (

−1
) ∗ 100
• Change in industrial production ∆ = ind_prod − ind_prod−1
• Change in consumer credit ∆ = con_credit − con_credit−1
• Change in money supply ∆ = m1_money − m1_money−1
• Change in US Dollar Index ∆ = usd_index − usd_index−1
• Change in corporate bond spread
∆ = (baa10y – aaa10y) − (baa10y−1 – aaa10y−1)
• Change in term premium
∆ = (tb10y – tb3ms) − (tb10y−1 – tb3ms−1)


2. Consider the following model:

{
= 0 + 1 + 2∆ + 3∆ + 4∆ + (1)
= 0 + 1 + 2∆ + 3∆ + 4∆ + 5∆ + (2)

ECON3371
Financial Econometrics
Undergraduate Programmes 2021/22



2

Due to simultaneous relationship between and that you have
discussed above, it is not possible to validly estimate the model by directly applying
OLS separately to each of the equations (the OLS estimates will be biased).
Estimate the model using 2SLS method. Report your results and interpret them:
comment on the sign, size and significance of the coefficients.
[7 marks]

3. Do your instruments (the lists of instruments in this case) satisfy two instrument
validity conditions: relevance and exogeneity?
[7 marks]

4. Conduct the Hausman test for endogeneity of stock returns and inflation. Based on
your results, was it justified to employ 2SLS methodology rather than OLS?
[7 marks]

5. Are equations 1 and 2 identified? Explain your answer. Was it possible to use ILS
instead of 2SLS?
[4 marks]

PART B: Cointegration of exchange rates
In this part you will consider several major currencies and test for cointegration among
them. While values of various countries’ currencies are affected by fundamentals of
those countries, there are also some common trends that shape the long-term
relationships across different exchange rates. You will explore those long-term
relationships here using two techniques: Engle-Granger and Johansen tests.

Download the file ‘summ_assig_data_B.xlsx’ that contains data on five nominal daily
exchange rates: the Canadian Dollar (CAD), Swiss Franc (CHF), Euro (EUR), British
Pound (GBP) and Japanese Yen (JPY), all relative to the US Dollar, over the 9-year
time interval from October 2012 until September 2021 inclusive. (Take natural
logarithms of exchange rates before proceeding with the exercises.)

1. Conduct Engle-Granger cointegration test pairwise for all potential pairs of five
given exchange rates (at 10% significance level). Report and interpret the results.
Is there evidence of cointegration among any pair of exchange rates?

Note: For the series to be cointegrated each of them needs to satisfy specific
requirements. To answer this question, conduct all necessary tests to check
whether the individual series satisfy those requirements prior to running the
cointegration test.
[10 marks]
ECON3371
Financial Econometrics
Undergraduate Programmes 2021/22



3


2. Briefly explain the main limitation(s) of Engle-Granger test and how Johansen test
resolves it.
[2 marks]

3. Conduct Johansen cointegration test for all five exchange rates (specifications for
the test: linear deterministic trend, 2 lags, 10% significance level). Report the test
results both based on the (1) trace and (2) maximum eigenvalue test statistics and
discuss (specifically: is there evidence of cointegration? if yes, how many
cointegrating relationships are there?). Are there any contradictions in results (1)
and (2)?
[8 marks]

PART C: Modelling and forecasting stationary time series
Suppose that you are a portfolio manager holding an equally-weighted portfolio
consisting of the 3 stock indices. The aim of this project is to examine the return
characteristics of this stock index portfolio.
Collect the closing daily prices of the 3 stock indices for the past 10 years from
Datastream. To summarise the data:
• Provide the names of the stock indices you have chosen to hold in your
portfolio, with their DataStream IDs.
• In the Appendix, plot the time series of the prices for the 3 stock indices.

Answer ALL of the following questions:
1. Choose an in-sample period and estimate the best-fit time series model for the
mean and variance process for your stock index portfolio returns. Carefully
discuss the procedure you have adopted to obtain the best model and interpret
your results. You can compare your modelling results with relevant academic
research articles.
[20 marks]
2. Perform out-of-sample forecasting of your index portfolio returns:
o Using the best mean and variance model specifications obtained from Question
1, forecast the mean and the variance process.
o Explain how you have produced the out-of-sample mean and variance
forecasts and what assumptions you have made.
o As an illustration, show mathematically how the forecasts are calculated for a
few steps ahead and compare it with the forecasts generated by Eviews.
[20 marks]

ECON3371
Financial Econometrics
Undergraduate Programmes 2021/22



4

3. Evaluate the forecast performance of your best mean and variance model against
a naïve benchmark model (such as the random walk). Use appropriate forecast
evaluation measures to assess the accuracy of your mean and variance forecasts.
Interpret the significance of your results from the perspective of a portfolio
manager who hold stock indices.
[10 marks]

Overall word limit: 4500

SUBMISSION INSTRUCTIONS

Your completed assignment must be uploaded to Ultra
no later than 12:00 midday on 25 April 2022.

A penalty will be applied for work uploaded after 12:00 midday as detailed in
the Programme Handbook. You must leave sufficient time to fully complete
the upload process before the deadline and check that you have received a
receipt. At peak periods, it can take up to 30 minutes for a receipt to be
generated.


Assignments should be typed, using 1.5 spacing and an easy-to-read 12-point font.
Assignments and dissertations/business projects must not exceed the word count
indicated in the module handbook/assessment brief.
The word count should:
▪ Include all the text, including title, preface, introduction, in-text citations, quotations,
footnotes and any other items not specifically excluded below.
▪ Exclude diagrams, tables (including tables/lists of contents and figures), equations,
executive summary/abstract, acknowledgements, declaration, bibliography/list of
references and appendices. However, it is not appropriate to use diagrams or
tables merely as a way of circumventing the word limit. If a student uses a table or
figure as a means of presenting his/her own words, then this is included in the word
count.
Examiners will stop reading once the word limit has been reached, and work beyond
this point will not be assessed. Checks of word counts will be carried out on submitted
work, including any assignments or dissertations/business projects that appear to be
clearly over-length. Checks may take place manually and/or with the aid of the word
count provided via an electronic submission. Where a student has intentionally
ECON3371
Financial Econometrics
Undergraduate Programmes 2021/22



5

misrepresented their word count, the School may treat this as an offence under
Section IV of the General Regulations of the University. Extreme cases may be viewed
as dishonest practice under Section IV, 5 (a) (x) of the General Regulations.
Very occasionally it may be appropriate to present, in an appendix, material which
does not properly belong in the main body of the assessment but which some students
wish to provide for the sake of completeness. Any appendices will not have a role in
the assessment - examiners are under no obligation to read appendices and they do
not form part of the word count. Material that students wish to be assessed should
always be included in the main body of the text.
Guidance on referencing can be found in the programme handbook and on Ultra.

MARKING GUIDELINES
Performance in the summative assessment for this module is judged against the
following criteria:
• Relevance to question(s)
• Organisation, structure and presentation
• Depth of understanding
• Analysis and discussion
• Use of sources and referencing
• Overall conclusions

PLAGIARISM AND COLLUSION
Students suspected of plagiarism, either of published work or the work of other
students, or of collusion will be dealt with according to School and University
guidelines.
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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