Homework SourseUsing the daily closing prices of American Express stock for
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 |
Solution
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.
