question 4

(a) Suppose the following time series model has been fit to historical data. (1-$1B ) Y, = 6+ 6, Assuming the parameter values, p1 = 0.45 and # = 217.50. (1) Estimate the value of & in the model. (ii) Rewrite the ARIMA equation as a function of I. (iii) The first four observations are Y1 = 1000, Y, = 832, Y's = 946, and 14 = 1029. Assuming Y, = 1000 and e, = 0, perform the forecasts for period 5 and 6 (t = 5 and 6) if period 4 is the forecast origin. (b) The following autocorrelations (ACF) and partial autocorrelations (PACF) plots of a time series data are obtained after applying first non-seasonal differencing O 10 20 LAG 02 04 CB PACE -02 10 15 20 LAG (i) Based on the figures above, identify the model as ARIMA (p. d, q) with your justification. (ii) Write the general equation for the ARIMA model in part (b)(i), assuming the value of u is 0