EC7079 Financial Econometrics: Project Topics 2016/17 You are expected to complete one project as part of the assessment arrangements for EC7079. This project counts 50% of the final examination mark, and the remaining 50% is based on a two-hour written examination. Your project must be submitted through Blackboard by Wednesday, 18th of January 2017. Late submissions will be penalised according to the University regulations. Your paper should be no more than 3,500 words. Empirical results should be presented (usually in tables) in the body of the project itself. The full estimation/testing outputs must be collected in an appendix, each one clearly labelled, and submitted with your project. Plagiarism and collusion will not be tolerated. Select one of the following two topics. 1. Collect three di↵erent time series. Firstly, estimate the best-fitting univariate model on two of them. Which two you wish to estimate a model on is your choice. Secondly, investigate if there exist long-run steady-state equilibria amongst the same set of three series. If such equilibria exist, fit an appropriate vector error correction model (VECM) and interpret the estimation output carefully. This is an empirical investigation exercise. If you opt to do this question, you are not permitted to use any of the dataset I provided for your computer classes. You must collect your own data. Also, to prevent too much similarity, you are not permitted to choose two or more time series that have already been chosen by other students in this class. You are permitted to have one series that has already been taken. In order for you to know what series your fellow students have chosen, I have created a sign-in sheet that is placed at the reception desk in Astley Clarke Building. This sheet looks as follows: Student ID Series 1 Series 2 Series 3 12345678 Series code & freq. ˆFTSE, d. –AE-AZ, d. XUDLDS6, d. Data source Yahoo Finance IFS Bank of England 87654321 Series code & freq. –AE-AZ, d. XUDLDS6, d. ABK–HY6, d. Data source IFS Bank of England Datastream 13245768 Series code & freq. BSI.M.U2.Y.V.M10.X. ˆNQDXGMN, d. 60EF-ZF, m. Data source 1.U2.2300.Z01.E, ECB Yahoo Finance IFS You can put 'h' for hourly frequency, 'd' for daily, 'w' for weekly, 'm' for monthly, 'q' for quarterly, and 'a' for annual. In the above table, student whose ID is 87654321, is not permitted to use all the series he has chosen, as two of them have already been taken. In such case, he must select another one—he is permitted to keep one of the two common ones. The next student, whose ID is 13245768, is technically permitted to use all three series he has chosen. But he has made life very di"cult for himself, as not all series have the same frequency. The first series with a long series ID code is monthly data on monetary aggregates 1on Euro area, and his third choice is also monthly. However, his second series is of daily frequency. In order to test for cointegration and potentially estimate a VECM, he will need to convert the daily series into monthly frequency. As not all months have the same number of working days, this will be a time-consuming task indeed. From this Wednesday, I will copy the sign-in sheet late afternoon, type up whatever has already been inputted, and will either put it on Blackboard or email it to you daily, or every few days after the term ends, till Friday 16th of December. Of course, this doesn't mean you have to select your series by Friday 16th. There are millions of financial time series data available through various sources online. Much of it is freely available, and we have access to Datastrem, UK Data Archive, Bloomberg, and so on through the University's digital library. When fitting a univariate model on each series, think back on all the univariate processes that you have learnt in this course, starting from stationary ARMA(p, q). Note that if a series is a unit root process, you need to di↵erence it su"cient number of times to make it stationary before you can estimate any model on it. Also, I shall advise you to consider the possibility of changing conditional volatility for high-frequency financial time series. 2. Simulate stationary ARMA(p, q) processes of your choice, with GARCH(m, r) errors if you so choose. Ensure to fix the seed of the random number generator. Find the power of the Augmented Dickey-Fuller t-test. How does the Type II error change as the parameter values of ARMA (and GARCH) processes change? Also, how does the Type II error change as the sample size increases? This question is a simple simulation exercise. If you simulate a stationary time series, and conduct the ADF test on it, you need it to reject the null hypothesis of a unit root process. If you are failing to reject it for a substantial proportion of the time, this indicates that the ADF test lacks power. In the computer class, due to the limited time available, the number of replications was a mere 500. However, in simulation exercises, this certainly is not enough to find convergence. I would recommend at least 20,000 replications for each specified series. With modern computing power, it should take no time at all. You can, of course, stick to a particular ARMA(p, q) process with one choice each for p and q. You will then need to change the parameter values for !1, !2, · · · , !p, as well as for ✓1, ✓2, · · · , ✓q, and see how the power of the test changes as the parameters of the process change. If you are being ambitious, you can throw in GARCH or GARCH-variant error term to simulate the behaviour of high-frequency financial time series. Whatever the process you opt to simulate, make sure that the stationarity and invertibility conditions for the level yt in ARMA(p, q), as well as the stationarity and non-negativity conditions for ht in GARCH processes, are met. If you choose to do Q2, you will need to submit the computer code to me as well as the project which summarises your findings. We will create a separate link on Blackboard for this purpose. Remember: we should be able to replicate your results exactly. Either using your computer code or the data you have chosen, if we were to conduct the same experiments/modelling, we should be able to obtain numerically identical results as the ones you report in your project. 2