Introduction to Time Series Econometrics (ECM3ITE).

Introduction to Time Series Econometrics (ECM3ITE). Assignment 3 This project is worth 40% of the total mark and should be handed in to me by 10am (in the lecture) on Thursday of week 12 (May 28). Late submission will not be accepted and no extensions will be given. This is a project where students should solve the questions independently. I am not allowed to help you on any aspect of the assignment, and I will not answer any questions directly related to the assignment, unless they are related to clarification of the content. Students can discuss the content of the project with their peers. However, the work on Eviews and report writing should be done individually and independently. Any form of plagiarism will be penalized according to the University policy. Your report should provide concise and relevant answers to all questions with question numbers, e.g. Q1. i) your answer, ii) your answer, and etc. The computer outputs should be attached as an appendix to your report or copy and pasted to the main report. In conducting statistical tests throughout, clearly state all relevant information, such as the null and alternative hypotheses, the distribution you use, the level of significance, and the decision rule (critical value or p-value), and the decision you make. Graphs and Tables should be self-explanatory, i.e. have titles and properly labeled axes. Your report may be typed or clearly hand-written on A4 pages, double-spaced (unclear handwriting may be unintentionally disadvantaged). Your report should not exceed 6 A4 Pages (excluding the appendix). You may shrink the size of graphs and tables but they should be legible. Note that “explain” or “discuss” type questions require concise and to-the-point answers (about 1/2 A4 double-spaced page maximum). Q1. The file data3a.xls contains the daily stock price (Pt) of Games Inc. from January 3, 2012 to December 31 2012. The total number of observations is 260. Use data3a.xls and do the following questions: i) Generate a new variable, the daily stock returns of Games Inc., Rt = 100 × log(Rt/Rt-1). Report the descriptive statistics (No of obs, Mean, SD, Min, Max) and histogram for both variables, Pt and Rt. Explain the Jarque-Berra test result. ii) Draw line plots for the time series Pt and Rt separately. iii) Using the ARCH LM test, test for the presence of conditional heteroskedasticity in the return, Rt. (Choose 4 lagged squared residuals for the test.) Clearly write the ARCH model and the null and alternative hypotheses, and discuss the test result. Q2. The file data3b.xls contains the daily stock price (Pt) of Toys Inc. from January 3, 2000 to January 31, 2012. The total number of observations is 3152. Use data3b.xls and do the following questions: i) Generate a new variable, the daily stock returns volatility of Toys Inc., Rt = 100 × log(Rt/Rt-1). Report the descriptive statistics (No of obs, Mean, SD, Min, Max) and histogram for both variables, Pt and Rt. Explain the Jarque-Berra test result. ii) Draw line plots for the time series Pt and Rt separately. iii) Using the ARCH LM test, test for the presence of conditional heteroskedasticity in the return, Rt. (Choose 4 lagged squared residuals for the test.) Clearly write the ARCH model and the null and alternative hypotheses, and discuss the test result. iv) Estimate the GARCH(1,1) model for the return volatility of Toys Inc., and plot the conditional variance estimates. Discuss the estimation result. v) Estimate the Threshold GARCH(1,1) model. Test if there is any evidence of asymmetric volatility or leverage effect. Clearly write the TGARCH model and the null and alternative hypotheses, and discuss the test result. vi) Test for the presence of return-risk relationship using GARCH(1,1)-M model. Estimate all three forms of volatility in the return equation, i.e. the conditional standard deviation, the conditional variance or the log of the conditional variance. What do you conclude? Does the time varying premium exist? Attach the computer output as an appendix to your report.