Eco $309-$Sp$24-$Assignment $1$ due by midnight on Wednesday Feb $7,2024$

Total points $125.$ Submit through D$2$L in Word$/$Excel format, single or multiple files. Must show

your work, answer all parts of the question, and write necessary explanations to earn full points.

You must use Excel to solve this numerical problem $($project$).$

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

ABC$$s sales in $millions.

Period Sales$($Y$)$

$165$

$270$

$375$

$480$

$575$

$670$

$785$

$880$

$988$

$1090$

$1185$

$12100$

$13105$

$14102$

$1598$

$16105$

$17108$

$18115$

$19118$

$20120$

$21122$

$22128$

$23130$

$24125$

$25132$

$26135$

$27138$

$28145$

$29140$

$30138$

$1.$ Plot the data using Excel $($insert$,$ Chart, scatter, lines...$)$ showing the trend line in the

plot. Comment on the visible features in the plot. Does it look stationarity and$/$or

Seasonality? Why or why not?

$1$

$2.$ Calculate the autocorrelation coefficients r$1,$ r$2,$ r$3,$ r$4,$ r$5,$ r$6,$ and r$7$ for the above series and

plot the $$Correlogram$$ using Excel. What do the autocorrelation coefficients tell you

about the time series?

$3.$ Create a table of first differences of the series $($Yt$-$Yt$-1).$ Plot the first differenced series

and comment on its stationarity.

$4.$ 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$(4).$

$2$