1. You are to download Bitcoin/US Dollar spot rate from 01/01/2013 to 31/12/2018 using monthly data from the Bloomberg terminal. Then, answer the following questions:

(a) Box-Jenkins methodology involves primarily 3 stages of model building: identification, estimation and diagnostic checking. For the given series, obtain a plot of the log returns and comment on the graph.

(b) Analyse the correlogram structure and comment on the structure of the data.

(c) Express the estimated ARMA(1,1) model in equation form.

(d) What is the value of the BIC and AIC for ARMA(1,1) model?

(e) Let us suppose that it is plausible that the model specification can take the form of ARMA(0,0) to ARMA(3,3). Use AIC and BIC to identify the best model. Your outputs should consist of two 4x4 matrices for AIC and BIC. Express the chosen model in equation form.

2. Assume that the trivariate series of daily exchange rates of US dollar, Euro and Yen against the British pound follows a VAR model. Download these exchange rates using daily frequency from January 2000 to December 2018 from the Bloomberg terminal. Construct continuously compounded returns series for these exchange rates and perform the following tasks:

(a) Choose the best VAR model using the BIC and AIC criteria and explain your reasoning.

(b) Estimate the final model and write down your fitted model. Examine and interpret some of the interesting characteristics. Find the R2 for your preferred model and interpret.

(c) Conduct a Granger-Causality (GC) test in a VAR(1) with no constant and compare this with your preferred VAR(p) model.

(d) Draw the impulse response diagrams and interpret your results.

3. Download the data file Brent Crude Oil (CO1) from the Bloomberg terminal. The data should contain historical oil prices for generic Brent Crude Oil that is sampled monthly from 01 January 2000 to 31 December 2018. In addition, you should also download the historical futures price (Futures Trade Price) for the same period. An estimable linear regression can be specified as: st = beta0 + beta1ft-1 + ut, where ft and st are the natural logarithms of Ft (the nearby futures price) and St (the spot price) for the Brent Crude Oil contract traded at the Intercontinental Exchange (ICE). Note that ut is an error term.

(a) Plot Ft-1 and St on the same graph. Indicate on the graph any major economic events. Additionally, using an Augmented Dickey-Fuller test and selecting the relvant lag length using BIC, assess whether ft-1 and st are unit root processes.

(b) Using the Engle-Granger 2-step method, assess whether st and ft-1 are cointegrated. If st and ft-1 are cointegrated, what does this imply?

(c) Discuss the economic rationale behind the result in 3(b). Also, briefly comment on how this result compares with relevant economic literature. Some useful references include:

Crowder, W.J., and Hamed, A. (1993): ‘A Cointegration Test for Oil Futures Market Efficiency,’ Journal of Futures Markets, 13:933-941.

Kellard, N., Newbold, P., Rayner, A. and Ennew, C. (1999), ‘The Relative Efficiency of Commodity Futures Markets’, Journal of Futures Markets, 19:413-432.

(d) Assuming that the series are cointegrated, use the ‘general to specific’ methodology to estimate an ECM (Error Correction Model). Briefly comment on the properties of your final ‘preferred’ model including discussion of short and long run elasticities.