Jill Smith, who has joined recently as the forecasting manager for ABC company, is interested in

developing quarterly forecasts for one of the company's key products. She has collected data on

quarterly sales for this product for the past $5$ years and they are given in below.

Quarterly Sales Data for $2007-2011$

Jll decides to use Holt's method with seasonality and trend with the initial estimates of level and trend

as $600$ and $50,$ respectively. She also decides to use the first $4$ years of data $(2007-2010)$ for determining the

smoothing constants $($ and $)$ and use the $2011$ data for validating the forecasting method and the chosen

smoothing constants.

$($a$)$ Using the data for the years $2007-2010,$ prepare the initial estimates of the seasonal factors for each

quarter.

$($b$)$Using a spreadsheet, develop and select a set of good smoothing constants for both $($ and $)$ for Holt's

method. Use the error measures bias and STD to test your parameters. Run your tests using data for years

$2007-2010.$ Use the following combinations of the smoothing constants for the tests:

$(,)=(0\mathrm{.}1,0\mathrm{.}1)$;$(0\mathrm{.}1,0\mathrm{.}2)$;$(0\mathrm{.}1,0\mathrm{.}3)$;$(0\mathrm{.}2,0\mathrm{.}2)$;$(0\mathrm{.}2,0\mathrm{.}3)$;$(0\mathrm{.}3,0\mathrm{.}3)$

$($c$)$ Select the two best pairs of values for the smoothing constants $($ and $)$ obtained from part $($b$)$ to

prepare the quarterly forecasts for $2011.$ Using the $2011$ actual sales data, validate these forecasts. Use bias,

standard deviation of forecast error, and tracking signals for the validation.

$($d$)$ Suppose Jill wants to try out simple moving average forecasting method, by averaging the past four

quarter's deseasonalized demands. For example, $2011$ Quarter $1$ deseasonalized forecast will be the

average of the $2010$ s deseasonalized quarterly demands. Using the moving average method, prepare the

quarterly forecasts for $2011.$ Compare these forecasts with those obtained in part $($c$)$ using the three

forecast errors. Are they better than the forecasts obtained using Holt's method? Why or why not?

$($e$)$ What forecasts, including estimates of their accuracy, should Jill present to her VP for sales for the year

$2012?$