THE UNIVERSITY OF NEW SOUTH WALES
School of Economics
Term 2 2022
Copyright By PowCoder代写 加微信 powcoder
FINANCIAL ECONOMETRICS
CASE STUDY PART 2
1. This is an individual assessment. You MUST produce and submit your own work. You
MUST view and sign the student declaration form.
2. Dataset: same company data and sample period as the one you have studied in Case Study Part
3. Submission Deadline: Friday Week 11 (August 12th 05:00 PM)
4. A submission link for each ‘Member’ number will be available from Moodle
5. IMPORTANT. There are TWO problems. Each worth 40 points. Nominate (choose) ONE of
the problems that will be fully marked. Your 30% of the marks will be based on this problem.
The remaining 10% will be based on your ‘reasonable’ attempt at the remaining problem.
• Reasonable will be judged based on your general understanding of what needs to be done,
and your understanding of the methodology and the theory and application. But we will
NOT FULLY CHECK THE CODES AND THE COMPUTATIONS. Theoretical results
will be checked.
6. Total marks: 80. This score will be weighted 40% for your total grade (30% for the
nominated problem, 10% for the other).
7. Attach your PYTHON code and output as Appendix.
8. RULES ON OPEN BOOK TAKE HOME ASSESSMENT: You have access to all resources
to work on the case study questions. However, any use of external resources MUST be cited
and referenced in your answer paper. This includes any textbook(s)/journal articles material
and any other internet resources. However, you cannot use someone else’s (any third party)
work as your own.
The UNSW rules and policies on Academic Integrity and Plagiarism apply. Collaboration
with others will be considered as cheating and may result in serious academic misconduct
penalties.
ALL SUBMISSIONS WILL BE CHECKED FOR PLAGIARISM
9. Show all the necessary derivations of the analytical results. Your discussion and answers should be to
the point.
10. No need to include the Python output in the answers. Only report the information required to answer
the specific questions. The Python code and output should be put at the end as an Appendix.
GOOD LUCK!
Problem I. Computing application [Total 35 marks allocated as shown below]
In this application you will use daily data on your company returns together with the S&P500 returns over the
same sample period as in PART I.
A. Set your in-sample or learning period to start from the first observation up to and including February 28th 2020.
Denote this sample size T1. Set the forecast (evaluation) period to be the remaining observations from March
1st, 2020 to the last observation. There are T − T1 observations in this forecast period. Use the following
methods to choose and estimate suitable forecasting models using the in-sample data only:
(i) Three months of average daily returns.
(ii) A Reg-AR(1): a regression with the lag 1 market index return added to a an AR(1) model for your
company return.
(iii) A CAPM Model for the excess returns on your company stock.
(1) [3 Marks] Report and discuss the estimates from each model specification above.
(2) [5 Marks] Generate moving origin (also knows as static forecasts) horizon 1-day forecasts for each obser-
vation in the forecast sample (the remaining T − T1 of the sample) from all methods above. Assess the
accuracy of these forecasting methods using plots, RMSFE and RMAFE.
Recall. The Root-mean-square-forecast-error (RMSFE) and the Root-mean-absolute-forecast-error (RMAFE):
(fes,s+1)2,
where h = T − T1, T the sample size, and T1 is the last observation in the training sample. Here the last
25% observations make the hold out sample T1 + 1 to T . The forecast error is the difference between the
value of the return at time (s+ 1) and its forecast ys+1|s made at time s
fes+1,s = ys+1 − ys+1|s, where s = T1, · · · , T − 1.
B. Given the Reg-AR(1) model in (A) for your company asset return series, assume Gaussian errors and fit the
following conditional volatility models: (i) GARCH(1,1), (ii) GJR-GARCH(1,1) and (iii) EGARCH(1,0) using
the first T1 of sample data.
(1) [7 Marks] Report the variance equations estimates and draw the news impact curves (NIC) from the three
conditional volatility models above. Comment on the shapes of the NICs.
(2) [6 Marks] Using a forecast origin of day T1, generate h-step-ahead forecasts of volatility, for h = T1 +
1, · · · , T , and for the volatility models (i), (ii) and (iii) in B. Comment and compare the plots of these
volatility forecasts.
(3) [4 Marks] Using a forecast origin of day T1, generate h-step-ahead forecasts of volatility, for h = T1 +
1, · · · , T , for the exponentially weighted moving average (EWMA) model with 1 − λ = 0.94. Add the
forecast series to your plot in B.(2). Compare the EWMA volatility forecasts series with the three forecast
series in B.(2).
C. Conditional volatility is unobservable which makes a direct comparison between forecasted volatility and actual
volatility impossible. GARCH forecasts can be evaluated using observable proxies for conditional volatility.
(1) [5 Marks] Generate 1-step-ahead forecasts of volatility using two proxies: (1) sample standard deviation
(all previous data) s(all past data), (2) sample standard deviation using the previous 25 observations s(25).
Add all these forecasts to your plot from B.(3).
(2) [5 Marks] Assess the accuracy of each model’s forecasts using volatility proxies 1 and 2. Which models
did best overall? Did the proxies agree on which were the best models over the whole data period and
especially around financial periods?
Problem II [Total of 35 marks allocated as shown below]
Suppose that your company returns, denoted {yt}, are generated by the following process:
yt = ϕ0 + ϕ1yt−1 + δσt−1 + ϵt + θ1ϵt−2 + θ2ϵt−4, where, |ϕ1| < 1, |θ1|+ |θ2| < 1, ϵt|Ωt−1 ∼ WN(0, σ2t ), σ2t = α0 + αϵ t−1It−1 + βσ α0 > 0 , α > 0, β > 0, γ > 0, α+ β +
where Ωt−1 denotes information available at time t − 1. It−1 is a binary random variable: It−1 = 1 if ϵt−1 < 0, and It−1 = 0 if ϵt−1 ≥ 0 Divide the sample data, 1, · · · , T into an estimation sample, 1, · · · , T1 and an evaluation sample T1 + 1, · · · , T . We are interested in comparing models pre- and post- Covid19. To do so, let T1 be the observation corresponding to February 28th 2020. A. [4 marks] Derive the analytical expression of the long-run (infinite horizon) forecast for yt. B. [4 marks] Derive the analytical expression of the unconditional variance var(yt). C. [4 marks] Estimate the model above using your company returns series from the Case Study Part 1 and the same sample period. Report the parameters estimates of the mean and variance equations. (i) [4 marks] Using the estimation results, compute a dynamic h-step ahead forecast for yT1+h and σ Place a 95% forecast interval around the point forecast of yT1+h, for h = 1, · · · , T−T1. Plot the forecasts and their forecast bands. (ii) [4 marks] Comment on the role of the GARCH component in the mean equation and its effect on the unconditional moments in (A.) and (B.) of the returns distribution. (iii) [4 marks] Find the empirical estimate of the 5% significance level conditional Value-at-Risk for T + 3. Assume that the total portfolio investment is normalized to $1 Million. (iv) [4 Marks] As a market analyst, you are interested in measuring how long news travel and stay in the returns series and thus in the financial market. In your analysis, how long before an unexpected shock, like Covid19 negative shock, dies out or at least halves its effect? D. You met your classmates and you started discussing and comparing model spesifications for their data. Your best friends told you that the best models for their company returns are: Yt = 0.9Yt−4 + ϵt − 0.5ϵt−1, ϵt ∼ N(0, 1) (1) Yt = Yt−1 + ϵt − 0.4ϵt−1, ϵt ∼ N(0, 1) (2) (a) [2 marks] Are the model specifications in (1) and (2) stationary and invertible for the computed parameter estimates? Explain. (b) [5 marks] Write down the AR(∞) representation of the two specifications in (1) and (2). Determine the values of the first three autoregressive weights and give the general formula for the other higher order (c) [5 marks] How would you characterize the kind of long-run behavior implied by each of the two models? In particular compare the impulse response functions, discuss whether the process is stationary and, if so, give its unconditional mean and unconditional variance. 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com