$**$ PLEASE PROVIDE ANSWERS TO TABLE AS WELL$**$Exercise $5\mathrm{.}5$

A firm experienced the demand shown in the following table.

Fill in the table by preparing forecasts based on a five$-$year moving average, a three$-$year moving average, and exponential si

$w=0\mathrm{.}3).($Note: The exponential smoothing forecasts may be begun by assuming widehat$(Y{)}_{t+1}=Y_t.)$

The following table shows the square errors, $(Y_t-$widehat$(Y{)}_{t-1}{)}^2,$ for forecasts from $2005$ through $2009.$ Exercise $5\mathrm{.}5$

A firm experienced the demand shown in the following table.

Fill in the table by preparing forecasts based on a five$-$year moving average, a three$-$year moving average, and exponential smoothing $(w=0\mathrm{.}9$ and

$w=0\mathrm{.}3).($Note: The exponential smoothing forecasts may be begun by assuming widehat$(Y{)}_{t+1}=Y_t.)$

The following table shows the square errors, $(Y_t-$widehat$(Y{)}_{t-1}{)}^2,$ for forecasts from $2005$ through $2009.$

Fill the table by calculating the root mean square error $($RMSE$)$ for each of the methods.

Square Error

Based on the RMSE criterion, which of the forecasting methods is the most accurate?

Exponential smoothing $(w=0\mathrm{.}9)$

Three$-$year moving average

Exponential smoothing $(w=0\mathrm{.}3)$

Five$-$year moving average

A firm experienced the demand shown in the following table.

Fill in the table by preparing forecasts based on a five$-$year moving average, a three$-$year moving average, and exponential smoothing $($w$=0\mathrm{.}9$

and w$=0\mathrm{.}3$

$).($Note: The exponential smoothing forecasts may be begun by assuming Y$$t $+1=$Yt

$.)$

Year

Actual Demand

Moving Average

Exponential Smoothing

$(5-$year$)$

$(3-$year$)$

$($W $=0\mathrm{.}9)$

$($W $=0\mathrm{.}3)$

$20001,300$

$20011,325$

$20021,375$

$20031,370$

$20041,390$

$20051,435$

$20061,425$

$20071,440$

$20081,480$

$20091,465$

$2010*$

The following table shows the square errors, $($Yt$$Y$$t $-1)2$

$,$ for forecasts from $2005$ through $2009.$

Fill the table by calculating the root mean square error $($RMSE$)$ for each of the methods.

Year

Square Error

Moving Average

Exponential Smoothing

$(5-$year$)$

$(3-$year$)$

$($W $=0\mathrm{.}9)$

$($W $=0\mathrm{.}3)$

$20056,8893,2492,2096,241$

$20062,116729252,025$

$20071,6815761962,116$

$20084,6242,2091,6815,184$

$20099612891211,225$

RMSE

Based on the RMSE criterion, which of the forecasting methods is the most accurate?

Exponential smoothing $($w $=0\mathrm{.}9)$

Three$-$year moving average

Exponential smoothing $($w $=0\mathrm{.}3)$

Five$-$year moving average