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ECMT2130 Financial Econometrics

Semester 2, 2023

GROUP PROJECT

DUE: 11.59pm Friday, 3 rd of November 2023

Instructions

•   This is a group assignment which accounts for 20% of your final mark.

•   You can either hand-write or type your answers, but please compile all your answers in one single PDF file and submit it via a file upload in Canvas. You can only submit your work once, so please double check everything before submitting.

•   There are 15 questions in this assignment, and please attempt all questions.

•   I will randomly select 5 questions to mark, and each question is worth 4 points. The total number of points of this assignment is therefore 20. The grading will be based on the

completion and general quality of your submission.

•   Refer to the group spreadsheet (link here:Spreadsheet) to find out which ASX200

company your group has been allocated to. Failure to work with the correct series will   result in a 50% loss of the entire mark of the assessment, i.e., your maximum mark will be 10 (instead of 20).

•   Answer all questions in aneat PDF document (no other extensions accepted). Use Times New Roman font size 12 throughout the report and normal margins. Make sure any

pictures included in the document are pasted correctly: your report should look neat, clean and easy to navigate.

•   Only the group leader is required to submit the final report. Please, make sure to include a cover sheet with the SIDs of the group members, their signatures and the series assigned   to the group.

•   Based on the University late policy, a late submission is subject to a penalty of 5% (of the total points) per calendar day; and work submitted more than 10 days after the due date

will receive a mark of zero.

•   You are free to use any econometric software and/or Excel. It is also fine to work with a combination of them. If you are using R, submit your script. If you are working with

Excel, make sure to include the spreadsheet in xslx format with brief explanations of which question you are doing. If you are working with anything else, make sure to

include commands and results in aneat document. Your software work file should be separate from the main report with the solutions (so, you’ll likely submit two files).

QUESTIONS

Throughout the assignment, I will symbolise the series of (close) share price as pt  and the

corresponding series of returns with Rt. The timespan you should use is the one specified in the “Data.R” script provided, i.e., from the 1st  of January 2020 until the 1st  of October 2023.

Using your assigned financial time series, answer the following questions:

1) Provide a brief overview of what the company you have been selected does. Make sure to include the goods/services it commercialises, number of clients, where it operates in the

world, its main competitors and its last financial figures. Do not surpass more than half a page on this question.

2) If the Efficient Market Hypothesis (EMH) is true, do you expect to find a good model to forecast the conditional mean of pt? Briefly explain.

3) Plot pt. Make sure to include labels on they and x axes, as well as a title. Describe its main features from a classical decomposition perspective.

4) Calculate the average, standard deviation, minimum, maximum, skewness and kurtosis of your series of prices and return series over the time span specified. Place them all on aneat   table, preferably prepared in Excel or equivalent (do not copy and paste R output). Interpret  the kurtosis of your series.

5) Propose a histogram for pt  and another for Rt. Using the graphs and the basic statistics

obtained in question 4, indicate whether the sampling distribution of price and return are

visually likely to be normally distributed. Feel free to overlay a normal distribution on top of the histograms to strengthen your argument and/or use statistical tests of normality.

6) Calculate the Sharpe ratio for Rt  and for the market proxy (ASX200 returns). You will    need to find the return of the risk-free asset for the relevant period. Briefly justify why you selected such a risk-free rate.

7) Calculate the alpha and beta of your assigned share. Interpret both values. Do you have

evidence pro or against the CAPM in your case? Make sure to indicate the null hypothesis of your tests in the explanation. Hint: be careful herewith the number of observations for both   dependent and independent variables.

8) Fit the following modelstopt :

(i) Drift.

(ii) Mean.

(iii) Naïve.

(iv) 5-MA.

Evaluate, using the in-sample RMSE, which model fits the data best. Plot a graph of the

series of prices and fitted values of your best model in the same picture. Forecast the next two days of data using your favourite model.

9) Fit the following modelstopt :

(i) Simple Exponential Smoothing (SES).

(ii) Holt’s linear trend.

Which model fits the data better using the MAPE? Justify your choice. Forecast the next two days of data using your favourite model. Make sure to include 95% confidence intervals around the forecasts.

10) Is Rt  a stationary series? Use the KPSS test, as well as the ACF plot to justify your claim. Apply an appropriate level of differencing, if necessary. If you do, show that the transformed  series is now stationary using the KPSS test.

11) Using the ACF and PACF of the (potentially differenced) return series, propose a suitable ARMA model. Explain how you obtained your answer and write out the model specification. Compare this model with a simple model regressed on a constant only (with specification

Rt  = μ + εt ). Use an information criterion of your choice to decide.

12) Using your preferred ARIMA(p, d, q) model, produce forecasts for the next 5 days. Make sure to calculate the 95% forecasting intervals.

13) Using actual data from Yahoo Finance, pick the model (from Q8, Q9 and Q12) that best forecasted the next five business days of Rt. Contrast this with what you expected in Q2.

14) Using Rt , propose an ARCH(1), ARCH(2) and ARCH(3) model. Are the parameter

conditions met? Which one seems most appropriate for your data? Justify your answer. Plot the fitted variance of the returns.

15) Using Rt , propose a GARCH(1,1) model. Plot the fitted variance of the returns. Are the period(s) of high observed volatility in the graphs in Q3 consistent with the predicted

volatility generated by the GARCH(1,1) model?