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BE-333-6: Empirical Finance

Coursework 2

Instructions: This coursework assignment (research report) must be submitted electronically via FASER by the due date and time. When submitting your coursework assignment you must provide one Microsoft Word or PDF file containing your written/text answers to the questions. In your answers to the questions below, you should present your Eviews equation estimation output as it would be in published academic papers. (Examine several such papers, the approaches to presentation are fairly standard.) Raw Eviews output should be included only in an Appendix.  

The report should not exceed 2000 words in length. It should have a clear introduction and a conclusion.  You should ensure that you have fully acknowledged the work of others in the body of the text and include a full list of references for all articles, books and other sources (e.g. Internet sites) that have been cited in the assignment. Coursework will be processed with plagiarism detection software. Marks will also be given for the presentation of your work.

The data required for the coursework is contained in the excel file `Coursework_2.xls’ in the coursework section on Moodle. The file contains daily return and 5-min realised variance data for RUSSEL2000 from January 2000 to December 2017 that we will use to estimate and forecast the volatility of RUSSEL2000.  

Question 1 (10 points)

Describe the notion of non-stationarity and explain the concept of cointegration. Discuss how a researcher might test for cointegration between non-stationary variables using the Engle-Granger approach.

Question 2 (20 points)

Consider the observations for Realised Volatility (RV, square root of realized variance) for years 2000 to 2015 (i.e. leave years 2016-2017 observations for out-of-sample forecasting) and build an appropriate ARMA model for the RV series. Explain how you arrived at your chosen model.

Question 3 (10 points)

Based on the model you found in Question 2, forecast the realised volatility (square root of RV) for the last two years’ observations in your sample (2016-2017). Plot your forecasts against the actual realizations of the volatility series (RV proxy), as well as the forecast errors (i.e. actual – forecast). Interpret the results.

Question 4 (20 points)

Consider the observations for the related stock index return series (RUSSEL 2000) for the period ranging from 2000 to 2015. Build an appropriate ARMA model and test for ARCH effects in the series of daily returns.

Question 5 (30 points)

Using the observations for years 2000 to 2015, estimate the following models from the GARCH family, selecting the appropriate lags:

· GARCH with normal innovations

· GJR with normal innovations

· a specification of your choice

always using as the conditional mean equation the ARMA specification that you identified in Question 4 above.  For each of these models, forecast the daily volatility (square root of variance) for the last two years in your sample. Plot your forecasts against the actual realizations of the variable (realised volatility proxy), as well as the forecast errors (i.e. actual – forecast). Interpret the results.

Question 6 (10 points)

Compute the MSE, MAE and MAPE for all 4 models which you estimated (i.e. the ARMA model from Question 2 plus the 3 GARCH models from Question 5. According to each of these criteria, which model forecasts best and which model forecasts worst?