The Following Time Series Shows the Sales of a Particular

Essay

The following time series shows the sales of a particular commodity over the past 15 weeks. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Sales } \\\hline 1 & 1,123 \\\hline 2 & 1,157 \\\hline 3 & 1,138 \\\hline 4 & 1,120 \\\hline 5 & 1,130 \\\hline 6 & 1,132 \\\hline 7 & 1,188 \\\hline 8 & 1,151 \\\hline 9 & 1,129 \\\hline 10 & 1,118 \\\hline 11 & 1,125 \\\hline 12 & 1,147 \\\hline 13 & 1,162 \\\hline 14 & 1,190 \\\hline 15 & 1,137 \\\hline\end{array}$$
a. Construct a time series plot. What type of pattern exists in the data?
b. Use α = 0.3 to develop the exponential smoothing values for the time series and compute the forecast of demand for the next week.
c. Use trial and error to find a value of the exponential smoothing coefficient α that results in a relatively small MSE.