Questions:

1. The following data covers 30 periods (could be years quarters or months) for company ABC's sales in $millions.

Period	Sales(Y)
1	65
2	70
3	75
4	80
5	75
6	70
7	85
8	80
9	88
10	90
11	85
12	100
13	105
14	102
15	98
16	105
17	108
18	115
19	118
20	120
21	122
22	128
23	130
24	125
25	132
26	135
27	138
28	145
29	140
30	138

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?

2. Calculate the autocorrelation coefficients r₁, r₂, r₃, r₄, r₅, r₆, and r₇ for the above series and plot the "Correlogram" using Excel. What do the autocorrelation coefficients tell you about the time series?

3. Create table of the 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, and 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 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 a simple MA(4) forecast. Make a forecast for period 26 (one period beyond the sample) using DMA(4).