# 1. You have estimated the following ARMA(1,1) model for some time series data yt =0 . 036+0 .

1. You have estimated the following ARMA(1,1) model for some time series data yt=0.036+0.69yt1 +0.42ut1 +ut Suppose that you have data for time to t-1, i.e. you know that yt1 =3.4, and

ˆut1 = -1.3

a) Obtain forecasts for the series yfor times tt+1, and t+2 using the estimated ARMA model.

b) If the actual values for the series turned out to be-0.032, 0.961 0.203 for tt+1, t+2, calculate the (out-of-sample) mean squared error.

c) A colleague suggests that a simple exponential smoothing model might be more useful for forecasting the series. The estimated value of the smoothing constant is 0.15, with the most recently available smoothed value, St1 being 0.0305. Obtain forecasts for the series yfor times t+1, and t+2 using this model.

d) Given your answers to parts (a) to (c) of the question, determine whether Box–Jenkins or exponential smoothing models give the most accurate forecasts in this application