$1.$ The following data covers $30$ periods $($could be years or quarters or months$)$ for company

ABC$$s sales in $millions.

Period Sales$($Y$)$

$165$

$270$

$375$

$480$

$575$

$670$

$785$

$880$

$988$

$1090$

$1185$

$12100$

$13105$

$14102$

$1598$

$16105$

$17108$

$18115$

$19118$

$20120$

$21122$

$22128$

$23130$

$24125$

$25132$

$26135$

$27138$

$28145$

$29140$

$30138$

$4.$ 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 $26($one period

beyond the sample$)$ using DMA$(4).$