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EC912 Quantitative Methods. Mini-Project 2: Time Series. Your answer must be submitted by 23:59 on Monday 13th of March 2017. 1 Submission Details. Projects which violate any of the following constraints will be penalized by 15 points (out of 100). • The report should be a maximum of 2 sides of one A4. In addition to this, you can separately add up to 2 sides of one A4 containing tables and graphs. • Tables should include ONLY those results which are relevant for your discussion. • The preferred way of reporting parameter estimates from regression functions is an in-line equation, with standard errors in parenthesis, as in, Ybt = 0.439673 (0.13968) + 1.16446 (0.015067) Xt. (1.1) If you end up with a model with a very large number of terms on the right hand side, then report only the important estimates. • The project must be word processed, using 12 point Arial font and margins of at least an inch at top, bottom, left and right. • Do not add a cover page or a title to the report. • The project must be submitted using MyPlace. Late submission (except in exceptional medical circumstances and with prior agreement) will be penalized according to departmental policy which is: 1 day late 5% of the mark allocated deducted. 2 days late 10% of the mark allocated deducted 3 days late 20% of the mark allocated deducted 4 days late 40% of the mark allocated deducted 5 days late 100% of the mark allocated deducted 2 Project. The file santanderBBVA.gtl contains the weekly prices of two shares listed in the Madrid Stock Exchange. The shares correspond to multinational Spanish banking groups Santander Group and Banco Bilbao Vizcaya Argentaria (BBVA). The period under consideration is 1st of March 2000 to 27th of February 2017. Using Gretl, complete the following tasks. 1. For the BBVA series: • Evaluate whether or not the series is I(1). 1 • Transform the series into returns. Evaluate if the transformed series is I(1). • Using a histogram study the distribution of returns, and comment on whether the distribution exhibits thicker tails than the normal distribution. • Study whether or not the square of the series in returns exhibits persistence. • Given your previous answers, would you say that the series of BBVA in returns exhibits conditional heteroskedasticity? • Fit a GARCH(1,1) and a GARCH(2,1) to the BBVA time series in returns. Your model should include a lag of the dependent variable in the conditional mean. Use an information criteria to select one of the two models. For the selected model plot a graph of Residuals vs BBVA in Returns. Provide a brief description of the pattern of volatility in the series. 2. Produce a time series plot of the Santander and BBVA series in levels. On the basis of this plot alone, would you say that the two series are cointegrated? 3. Formally test if the Santander and BBVA series are cointegrated and, in so, report the value of the cointegration parameter. Discuss your results. 2

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