Answer Happy

1. (a) The following is the yearly coffee production in coded units) of a certain country from 2012 to 2020. Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 t 1 2 3 4 5 6 7 8 9 Ct 27 25 29 27 32 36 40 16 21 It is felt that the data can be fitted by the linear trend model, X4 = a + Bt + €t, where et ~NID(0,0%). Find that the least squares estimates of a and B, and hence forecast the value of 2021. [9 marks] (b) Assume we use the linear trend model in (a) and instead of linear regression, it is suggested to use the Double Exponential Smoothing (DES) method with exponential smoothing parameter a = 0.1 to do the forecast: St = aX+ + (1 - a) St-1, $123 = aS4 + (1 - a)522 a a = and Q+ = 2S– S121, be = 1^ a(Se – 5,2). The T step forecast at time t is Åt+s = qt + b47. = 20, bo = 6, calculate the one-step forecast for 2016 using the data in (a). Do you suggest to use simple exponential smoothing to do the forecast? Why or why not? [9 marks Given ao