FRED S&P 500 4,000 index 3,600 3,200 2,000 2,400 2,000 1,600 1,200 g 300 Jan 2012 Jan 2013 Jan 2014 Jan 2015 U.S. recessions are shaded; the most recent end date is undecided. Jan 2016 Source: S&P Dow Jones Indices LLC Jan 2017 Jan 2018 Jan 2019 Jan 2020 fred stlouisfe 2012 2014 2016 2018 2020 8,000,00 8,000.00 4,000.00 2,000.00 0.00 The two indices relate to the USA and the UK, respectively. Both indices are I(1). a) Given that the two series are I(1), is it possible for there to be a causal relationship between them? If it is possible, how would you test for the existence of such a relationship? [5 marks] < < and < b) Suppose that we then estimated the following pair of regressions: < [1] ft = 5000+50t + 0.1st (1000) (32) (0.02) < < - [2] Aft = 5 0.5(ft-1 ft-1) + 0.7Ast 0.2Ast1 + 0.1Aft-1 < (4.3) (0.1) (0.2) (0.34) (0.7) < where numbers in ( ) are the standard errors of the estimated coefficients. f represents the FTSE100 index and s represents the S&P 500 index. < < The residuals from regression (2) do not exhibit serial correlation or heteroskedasticity. < Given these results, what can be said about the relationship between the two indices? [35 marks]