Problem
(i) Briefly discuss why ARMA models might well be expected to arise in practice when analyzing a single time series.
(ii) A statistician working for the Central Bank in a small South American country wants to forecast money supply for the country. He only has monthly data of the seasonally adjusted series from July 1965 to February 1976 ready for the computer and figures for March and April 1976 in print. He wants to fit a simple time series model and is uncertain about whether to use an MA(1) or an AR(1) model. How would you advise him to decide on a model? He puts the computer-available data onto his computer and obtains an estimate of 0.5 for ρ1, the first-order serial correlation coefficient and 100 for the mean of the series. However, the machine loses the data whilst performing this calculation. The two remaining values for his series are 126 and 84 for March and April 1976 respectively. Using the available information and both of the two simple models, obtain alternative forecasts for money supply in May and June 1976.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.