Question: West Virginia Virtuoso Widgets has produced the following numbers of its worsted widgets over the past four and one-half years, with data reported quarterly:

Provide as much quarterly forecasting information about anticipated production levels of worsted widgets as possible, based upon this available data. Determine forecast values using (a) three-quarter centered moving averages, (b) five-quarter centered moving averages, (c) four-quarter centered weighted moving averages, with corresponding weights of 50%, 30%, 15%, and 5%, in reverse chronological order, and (d) exponential smoothing, given a smoothing constant of 40%. Then, compare the accuracy of each forecast by computing the measures (e) MAD, (f) MSE, and (g) MAPE, being sure to identify if any forecasting technique seems most accurate or reasonable based upon these measures. Finally, use seasonal trend analysis to determine the percentage change for the (h) third quarters and (i) fourth quarters from their respective average quarterly production levels for the worsted widgets; to do so, compute all possible four-quarter centered moving averages in order to calculate the corresponding seasonal effects.