$1$

$.$

$$The following data covers

$3$

$0$

$$periods

$($

could be years or quarters or months

$)$

$$for company

ABC

$$

s sales in $millions.

Period Sales

$($

Y

$)$

$1$

$6$

$5$

$2$

$7$

$0$

$3$

$7$

$5$

$4$

$8$

$0$

$5$

$7$

$5$

$6$

$7$

$0$

$7$

$8$

$5$

$8$

$8$

$0$

$9$

$8$

$8$

$1$

$0$

$9$

$0$

$1$

$1$

$8$

$5$

$1$

$2$

$1$

$0$

$0$

$1$

$3$

$1$

$0$

$5$

$1$

$4$

$1$

$0$

$2$

$1$

$5$

$9$

$8$

$1$

$6$

$1$

$0$

$5$

$1$

$7$

$1$

$0$

$8$

$1$

$8$

$1$

$1$

$5$

$1$

$9$

$1$

$1$

$8$

$2$

$0$

$1$

$2$

$0$

$2$

$1$

$1$

$2$

$2$

$2$

$2$

$1$

$2$

$8$

$2$

$3$

$1$

$3$

$0$

$2$

$4$

$1$

$2$

$5$

$2$

$5$

$1$

$3$

$2$

$2$

$6$

$1$

$3$

$5$

$2$

$7$

$1$

$3$

$8$

$2$

$8$

$1$

$4$

$5$

$2$

$9$

$1$

$4$

$0$

$3$

$0$

$1$

$3$

$8$

$4$

$.$

$$Run

$4$

$-$

period and

$5$

$-$

period moving average forecasts for the above sales data and

compare the forecasts using MAD, MAPE, MSE, RMSE. Forecast for one period

ahead

$($

beyond the sample

$)$

$.$

$$Also calculate the Mean Percentage Error

$($

MPE

$)$

$$for

MA

$($

$4$

$)$

$$and MA

$($

$5$

$)$

$$forecasts and discuss the systematic bias

$($

if any

$)$

$$illustrating with the

plot of actual vs forecasted values and plots of errors for both MA

$($

$4$

$)$

$$and MA

$($

$5$

$)$

forecasts. Why do you think such a systematic biases, if any, may occur?

$5$

$.$

$$Correct this bias by performing a Double Moving Average method with four periods

and plot the errors of DMA

$($

$4$

$)$

$.$

$$Calculate its MAD, MAPE, MSE, RMSE, and MPE

and compare with simple MA

$($

$4$

$)$

$$forecast$.$ Make a forecast for period

$2$

$6$

$($

one period

beyond the sample

$)$

$$using DMA

$($

$4$

$)$

$.$