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1. (70 marks) From any (reliable) data source choose a univariate time series of your interest, with at least 50 equally spaced data points. (Choosing a time series that has already been provided to you in this module, either as part of an application in the lectures or for the labs, will incur a penalty of 50% on this question.) (a) [15 marks] Explain why your chosen time series is of interest and discuss its features (for example, trend, structural breaks, cycle elements). Make sure to cite your data source and any references you may use. (b) [15 marks] Determine if your time series is stationary or not using the Augmented Dickey Fuller (ADF) test. Explain clearly what you are doing. (c) [25 marks] Use the Box-Jenkins procedure to obtain the most suitable model for your time series. Explain each step carefully. (Note that if the series is non- stationary, you need to use the appropriate transformation to make it stationary.) (d) [15 marks] Consider the "best" model you chose in part (c) and perform the Engle's Lagrange Multiplier (LM) test on the residuals to determine whether or not the residuals show conditional heteroscedasticity. Explain clearly what you are doing. (Note that if the series does not exhibit conditional heteroscedasicity, you still need to show and explain the results of the test. )