# Use Excel to solve this Numerical Problem

Must show your work, answer all parts of the question, and write necessary explanations to earn full points. You have to use Excel to solve this numerical problem (project).

1. The following data covers 20 periods (could be years or quarters) for company XYZ’s sales in \$millions.
 Period Sales(Y) 1 10 2 11 3 14 4 14 5 12 6 15 7 18 8 16 9 16 10 17 11 16 12 20 13 24 14 22 15 20 16 24 17 26 18 28 19 28 20 26

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(i) 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 have stationarity and/or Seasonality? Why or why not? (ii) Calculate the autocorrelation coefficients r1, r2, r3, r4, r5, r6, r7 and r8 for the above series and plot the “Correlogram” using Excel. What do the autocorrelation coefficients tell you about the time series (iii) Create a table of first differences of the series (Yt-Yt-1). Plot the first differenced series and comment on its stationarity. (iv) Run 2-periods and 3-periods moving average forecasts for the above sales data and compare the forecasts using MAD, MAPE, MSE, RMSE. Also calculate the Mean Percentage Error (MPE) for MA(2) and MA(3) forecasts and discuss the systematic bias (if any) illustrating with the plot of actual vs forecasted values for both MA(2) and MA(3) forecasts. Why did such a systematic bias occur? (v) 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 a simple MA(4) forecast. Make a forecast for period 21 (one period beyond the sample) using DMA(4).