ARMA:accurate forecasts using Mean-Square Error (MSE) criterion.VAR(1)
ARMA:accurate forecasts using Mean-Square Error (MSE) criterion.VAR(1) :impulse-response1. Two researchers are asked to estimate an ARMA model for a daily USD/GBPexchange rate return series, denoted xt. Researcher A uses Schwarzs informationcriterion (SBC) for determining the appropriate model order and arrives at anARMA(0,1). Researcher B uses Akaikes information criterion (AIC) whichdeems an ARMA(2,0) to be optimal. The estimated models are:Model by A: xt 0.38 0.10ut 1 Model by B: x t 0.63 0.17 xt 1 0.09 xt 2 where ut is an error term. You are given the following data for time until day z (i.e. t =z) xz = 0.31, xz?1 = 0.02, xz?2 = ?0.16 uz = ?0.02, uz?1 = 0.13, uz?2 = 0.19.a) Produce forecasts for the next 4 days for x (i.e. for times z + 1, z + 2, z + 3, z + 4)from both models.b) Suppose that the actual values of the series x on days z +1, z +2, z + 3, z + 4turned out to be 0.62, 0.19, ?0.32, 0.72, respectively. Determine whichresearchers model produced the most accurate forecasts using Mean-Square Error(MSE) criterion.2. Consider the following VAR(1) process where y1t denotes the growth in real percapita GDP and y2t is the inflation: y1t 0.5 0.3 y1t 1 u1t y 0.0 0.2 y 2t 1 v 2t 2t a) Consider the effect at time t = 0, 1, . . . , of a unit shock to y1t at time t = 0.Trace the impulse-response for the next two periods. Note the shock occurs inthe disturbance term (here in terms of u1t) b) Consider the effect at time t = 0, 1, . . . , of a unit shock to y2t at time t = 0.Trace the impulse-response for the next two periods (here in terms of v2t).