Question
Using the daily closing prices of American Express stock for a one year period, answer the following:
a. Using moving average method with span of 3, forecast the price of stock for the next trading day.
b. Repeat part a with a span of 10.
c. Which of the above two models do you recommend? Justify your answer.
Date Open High Low Close 15-Oct-03 49.01 49.11 47.76 48.30 16-Oct-03 48.30 48.81 48.04 48.38 17-Oct-03 48.38 48.49 47.59 47.84 20-Oct-03 47.95 48.09 47.69 47.92 21-Oct-03 48.28 48.73 48.21 48.40 22-Oct-03 48.40 48.40 46.97 47.04 23-Oct-03 47.68 47.89 46.70 47.63 24-Oct-03 47.40 47.78 47.07 47.62 27-Oct-03 48.01 48.25 46.60 46.75 28-Oct-03 46.60 47.54 46.46 47.54 29-Oct-03 47.54 47.71 47.05 47.35 30-Oct-03 47.56 47.58 46.45 46.52 31-Oct-03 46.90 47.20 46.64 46.93 3-Nov-03 47.37 47.40 46.79 47.23 4-Nov-03 47.18 47.20 46.75 47.12 5-Nov-03 46.82 47.36 46.82 47.31 6-Nov-03 47.10 47.82 46.86 47.37 7-Nov-03 47.75 47.75 46.43 46.50 10-Nov-03 46.40 46.45 45.84 46.08 11-Nov-03 46.10 46.10 45.13 45.48 12-Nov-03 45.44 46.18 45.27 46.02 13-Nov-03 46.03 46.03 45.60 45.80 14-Nov-03 45.51 45.78 45.08 45.33 17-Nov-03 44.40 44.51 43.53 43.93 18-Nov-03 43.95 44.70 43.85 44.48 19-Nov-03 44.45 44.97 44.27 44.88 20-Nov-03 44.25 45.15 44.25 44.40 21-Nov-03 44.41 45.04 44.35 44.90 24-Nov-03 45.10 45.30 44.74 45.15 25-Nov-03 45.38 45.49 45.27 45.35 26-Nov-03 45.36 45.89 45.36 45.73 28-Nov-03 45.76 45.95 45.59 45.71 1-Dec-03 45.99 46.34 45.82 46.05 2-Dec-03 45.80 46.04 45.63 45.80 3-Dec-03 45.94 46.21 45.83 45.99 4-Dec-03 45.72 46.24 45.68 46.07 5-Dec-03 45.90 45.95 45.45 45.50 8-Dec-03 45.56 46.15 45.56 46.15 9-Dec-03 46.23 46.24 45.58 45.70 10-Dec-03 45.74 45.79 44.98 45.19 11-Dec-03 45.08 45.43 45.05 45.25 12-Dec-03 45.40 45.55 44.95 45.20 15-Dec-03 46.15 46.15 45.29 45.31 16-Dec-03 45.48 45.84 45.22 45.27 17-Dec-03 45.30 45.38 44.80 45.00 18-Dec-03 45.60 46.86 45.40 46.77 19-Dec-03 47.12 47.43 46.88 47.21 22-Dec-03 47.21 47.46 47.15 47.44 23-Dec-03 47.48 47.70 47.30 47.68 24-Dec-03 47.68 47.93 47.62 47.88 26-Dec-03 47.88 47.89 47.77 47.83 29-Dec-03 47.92 48.50 47.85 48.50 30-Dec-03 48.33 48.39 48.12 48.29 31-Dec-03 48.31 48.39 47.89 48.23 2-Jan-04 48.43 48.55 47.73 47.75 5-Jan-04 48.08 48.33 47.82 48.17 6-Jan-04 47.95 48.33 47.93 48.25 7-Jan-04 48.44 48.44 48.08 48.39 8-Jan-04 48.48 48.73 47.80 48.25 9-Jan-04 47.85 48.30 47.80 47.89 12-Jan-04 47.89 48.30 47.59 47.70 13-Jan-04 47.80 48.00 47.43 47.87 14-Jan-04 47.95 48.90 47.95 48.75 15-Jan-04 48.90 49.75 48.65 49.68 16-Jan-04 49.68 50.03 49.60 49.91 20-Jan-04 49.85 50.29 49.75 50.24 21-Jan-04 50.02 50.49 49.75 50.40 22-Jan-04 50.25 50.50 49.97 50.00 23-Jan-04 50.15 50.64 49.54 49.96 26-Jan-04 49.96 50.95 49.53 50.95 27-Jan-04 50.95 50.95 50.43 50.48 28-Jan-04 50.88 51.40 49.57 49.75 29-Jan-04 50.24 51.30 50.17 50.95 30-Jan-04 50.95 51.97 50.74 51.84 2-Feb-04 51.89 52.99 51.88 52.54 3-Feb-04 52.50 52.94 52.10 52.51 4-Feb-04 52.26 52.60 52.00 52.26 5-Feb-04 52.06 52.36 51.89 52.08 6-Feb-04 52.35 53.14 52.02 53.06 9-Feb-04 52.85 53.63 52.85 53.11 10-Feb-04 53.00 53.45 52.54 52.85 11-Feb-04 52.65 53.98 52.49 53.71 12-Feb-04 53.62 53.65 53.01 53.35 13-Feb-04 53.40 53.65 53.01 53.65 17-Feb-04 53.52 53.87 53.37 53.68 18-Feb-04 53.69 53.88 53.31 53.40 19-Feb-04 53.65 53.84 53.29 53.40 20-Feb-04 53.43 53.50 53.02 53.16 23-Feb-04 53.10 53.28 52.70 53.06 24-Feb-04 53.06 53.22 52.71 53.18 25-Feb-04 53.05 54.50 53.05 53.58 26-Feb-04 53.35 53.64 53.21 53.39 27-Feb-04 53.30 53.86 53.22 53.42 1-Mar-04 53.42 53.91 53.35 53.65 2-Mar-04 53.35 53.90 53.35 53.41 3-Mar-04 53.35 53.63 53.18 53.49 4-Mar-04 53.40 53.61 53.29 53.36 5-Mar-04 53.10 53.62 52.77 52.77 8-Mar-04 52.87 53.39 52.78 53.14 9-Mar-04 53.05 53.30 53.05 53.18 10-Mar-04 53.15 53.25 52.17 52.19 11-Mar-04 51.65 52.64 51.52 51.53 12-Mar-04 51.65 52.38 51.39 52.12 15-Mar-04 51.87 51.88 50.90 50.95 16-Mar-04 51.28 51.43 50.12 50.65 17-Mar-04 51.10 51.26 50.80 51.00 18-Mar-04 50.90 51.90 50.85 51.56 19-Mar-04 51.56 51.71 51.06 51.08 22-Mar-04 51.00 51.00 50.07 50.21 23-Mar-04 50.45 50.66 50.15 50.21 24-Mar-04 50.38 50.49 49.66 50.03 25-Mar-04 50.24 50.36 49.64 49.95 26-Mar-04 49.95 50.40 49.81 50.03 29-Mar-04 50.33 51.06 50.23 50.86 30-Mar-04 51.15 52.02 51.10 51.91 31-Mar-04 51.76 51.91 51.54 51.85 1-Apr-04 51.85 52.42 51.68 52.20 2-Apr-04 52.75 52.75 52.20 52.43 5-Apr-04 52.33 52.60 52.23 52.59 6-Apr-04 52.35 52.45 52.26 52.40 7-Apr-04 52.45 52.64 52.25 52.38 8-Apr-04 52.58 52.82 51.90 52.14 12-Apr-04 52.06 52.64 52.00 52.26 13-Apr-04 52.40 52.45 51.32 51.40 14-Apr-04 51.00 51.23 49.45 49.80 15-Apr-04 49.80 50.26 48.90 49.75 16-Apr-04 49.95 50.71 49.53 50.58 19-Apr-04 50.42 50.60 50.01 50.21 20-Apr-04 50.17 50.27 49.50 49.51 21-Apr-04 49.10 49.88 49.01 49.88 22-Apr-04 49.58 50.91 49.53 50.78 23-Apr-04 50.58 50.64 50.20 50.27 26-Apr-04 50.28 50.31 49.89 50.28 27-Apr-04 50.35 50.78 50.11 50.15 28-Apr-04 49.92 49.98 49.04 49.04 29-Apr-04 49.05 49.50 48.73 49.04 30-Apr-04 49.10 49.35 48.81 48.95 3-May-04 48.99 49.46 48.98 49.39 4-May-04 49.35 49.91 49.20 49.31 5-May-04 49.20 49.75 49.20 49.52 6-May-04 49.27 49.47 48.68 49.18 7-May-04 48.70 49.27 48.41 48.49 10-May-04 48.30 48.64 47.50 48.25 11-May-04 48.11 48.60 47.95 48.14 12-May-04 48.00 48.38 47.32 48.21 13-May-04 47.90 48.70 47.89 48.47 14-May-04 48.47 49.03 48.42 48.86 17-May-04 48.50 49.30 48.20 48.77 18-May-04 48.78 49.05 48.72 48.99 19-May-04 49.09 49.66 48.71 48.84 20-May-04 48.85 49.44 48.85 49.33 21-May-04 49.34 49.97 49.33 49.63 24-May-04 49.82 50.00 49.66 49.93 25-May-04 49.80 50.50 49.51 50.46 26-May-04 50.15 50.58 49.90 50.25 27-May-04 50.60 51.18 50.49 51.02 28-May-04 50.92 50.95 50.47 50.70 1-Jun-04 50.65 50.72 50.25 50.60 2-Jun-04 50.85 51.08 50.51 50.92 3-Jun-04 50.76 51.01 50.56 50.75 4-Jun-04 51.00 51.25 50.90 50.98 7-Jun-04 51.15 51.50 51.10 51.45 8-Jun-04 51.23 51.68 51.15 51.67 9-Jun-04 51.45 51.61 51.11 51.23 10-Jun-04 51.38 51.40 51.17 51.20 14-Jun-04 50.80 51.19 50.80 51.05 15-Jun-04 51.47 51.49 51.01 51.22 16-Jun-04 51.19 51.60 51.16 51.51 17-Jun-04 51.40 51.60 51.20 51.46 18-Jun-04 51.47 51.97 51.45 51.96 21-Jun-04 51.81 52.18 51.45 51.50 22-Jun-04 51.28 51.65 51.14 51.50 23-Jun-04 51.36 51.45 50.95 51.39 24-Jun-04 51.20 51.32 50.75 50.96 25-Jun-04 51.00 51.35 50.90 51.35 28-Jun-04 51.44 51.50 50.92 50.94 29-Jun-04 50.94 51.42 50.90 51.27 30-Jun-04 51.12 51.60 50.80 51.38 1-Jul-04 51.37 51.77 50.98 51.33 2-Jul-04 51.33 51.48 51.08 51.24 6-Jul-04 51.00 51.19 50.76 50.83 7-Jul-04 50.85 51.65 50.85 51.01 8-Jul-04 50.95 50.95 50.20 50.27 9-Jul-04 50.52 50.57 49.80 50.01 12-Jul-04 49.85 50.05 49.42 49.71 13-Jul-04 49.58 49.66 49.22 49.49 14-Jul-04 49.30 49.72 48.87 49.25 15-Jul-04 49.40 49.44 48.76 48.90 16-Jul-04 49.20 49.20 48.63 48.73 19-Jul-04 48.95 49.00 48.30 48.45 20-Jul-04 48.35 49.12 48.22 49.12 21-Jul-04 49.35 49.65 48.34 48.35 22-Jul-04 48.00 48.47 47.70 48.33 23-Jul-04 48.00 48.30 47.91 48.11 26-Jul-04 48.11 49.00 47.95 48.90 27-Jul-04 49.10 49.50 49.10 49.44 28-Jul-04 49.45 49.94 49.24 49.89 29-Jul-04 49.93 50.20 49.85 49.96 30-Jul-04 50.03 50.25 49.92 50.25 2-Aug-04 49.80 50.40 49.62 50.28 3-Aug-04 50.28 50.28 49.76 49.91 4-Aug-04 49.65 50.50 49.59 50.21 5-Aug-04 50.17 50.21 49.50 49.55 6-Aug-04 49.55 49.80 49.27 49.34 9-Aug-04 49.34 49.57 49.30 49.30 10-Aug-04 49.45 50.17 49.45 50.09 11-Aug-04 50.09 50.23 49.85 50.13 12-Aug-04 49.95 50.17 49.45 49.47 13-Aug-04 49.50 49.60 49.29 49.35 16-Aug-04 49.35 49.64 49.30 49.42 17-Aug-04 49.75 49.91 49.52 49.73 18-Aug-04 49.65 50.03 49.61 50.03 19-Aug-04 49.90 50.04 49.56 49.83 20-Aug-04 49.66 50.01 49.63 50.00 23-Aug-04 49.83 50.04 49.69 49.70 24-Aug-04 49.90 49.95 49.56 49.75 25-Aug-04 49.80 49.99 49.56 49.95 26-Aug-04 49.97 50.21 49.90 50.12 27-Aug-04 50.12 50.18 49.97 50.00 30-Aug-04 49.80 49.96 49.63 49.63 31-Aug-04 49.80 50.02 49.55 50.02 1-Sep-04 50.00 50.24 49.85 50.11 2-Sep-04 50.05 50.50 49.99 50.47 3-Sep-04 50.42 50.64 50.26 50.26 7-Sep-04 50.50 51.10 50.49 50.99 8-Sep-04 51.05 51.13 50.80 50.94 9-Sep-04 50.94 51.01 50.70 50.90 10-Sep-04 50.90 51.37 50.80 51.33 13-Sep-04 51.30 51.74 51.27 51.49 14-Sep-04 51.26 51.38 51.02 51.33 15-Sep-04 51.33 51.33 50.86 50.90 16-Sep-04 50.92 51.13 50.76 50.90 17-Sep-04 51.19 51.49 51.09 51.40 20-Sep-04 51.20 51.35 51.03 51.16 21-Sep-04 51.25 51.56 51.22 51.48 22-Sep-04 51.08 51.25 50.77 50.87 23-Sep-04 50.95 51.10 50.82 50.87 24-Sep-04 50.82 51.45 50.81 51.21 27-Sep-04 51.05 51.17 50.58 50.65 28-Sep-04 50.81 51.00 50.71 50.83 29-Sep-04 50.83 51.38 50.75 51.38 30-Sep-04 51.28 51.57 51.28 51.46 1-Oct-04 51.47 51.96 51.32 51.65 4-Oct-04 52.60 52.71 51.85 52.63 5-Oct-04 52.88 52.94 52.50 52.76 6-Oct-04 52.75 53.27 52.74 53.27 7-Oct-04 53.27 53.44 53.02 53.07 8-Oct-04 52.78 52.98 52.09 52.25 11-Oct-04 52.27 52.70 52.27 52.53 12-Oct-04 52.22 52.77 52.12 52.71 13-Oct-04 52.71 52.85 52.01 52.15 14-Oct-04 52.15 52.34 51.55 51.71 15-Oct-04 51.93 53.20 51.89 52.50
Explanation / Answer
Using daily closing price of American Express stock for a one year and using moving average method with span of 3, forcast price of stock for the next trading day using Minitab is as follows
Moving Average for CP
Data CP
Length 253
NMissing 0
Moving Average
Length 3
Accuracy Measures
MAPE 0.880860
MAD 0.437347
MSD 0.327638
Forecasts
Period Forecast Lower Upper
254 52.12 50.9981 53.2419
With a span of 10 forecast of stock for the next trading year
Moving Average for CP
Data CP
Length 253
NMissing 0
Moving Average
Length 10
Accuracy Measures
MAPE 1.50244
MAD 0.74707
MSD 0.88183
Forecasts
Period Forecast Lower Upper
254 52.558 50.7175 54.3985
The shorter the time span used to create the average, the more sensitive it will be to price changes. The longer the time span, the less sensitive, or more smoothed out, the average will be.
