Question
The closing prices for DJIA for each trading day of the year is given in the table.
a. Using moving average method with span of 3 forecast the price of this index on the next trading day.
b. Repeat the model of part a with 10 and 15 day spans.
c. Which of the three spans appear to be more appropriate? Why?
Date Open High Low Close 15-Oct-03 9824.09 9901.64 9731.57 9803.05 16-Oct-03 9798.68 9838.53 9679.13 9791.72 17-Oct-03 9791.86 9833.12 9679.72 9721.79 20-Oct-03 9721.50 9816.97 9665.35 9777.94 21-Oct-03 9778.31 9824.90 9697.94 9747.64 22-Oct-03 9741.98 9741.98 9551.65 9598.24 23-Oct-03 9597.20 9661.05 9517.50 9613.13 24-Oct-03 9600.98 9631.50 9463.28 9582.46 27-Oct-03 9584.54 9696.98 9553.80 9608.16 28-Oct-03 9609.72 9769.57 9592.54 9748.31 29-Oct-03 9747.05 9830.23 9663.27 9774.53 30-Oct-03 9772.01 9882.97 9719.20 9786.61 31-Oct-03 9786.75 9880.08 9745.94 9801.12 3-Nov-03 9802.46 9936.31 9792.60 9858.46 4-Nov-03 9857.49 9905.94 9770.46 9838.83 5-Nov-03 9837.64 9883.86 9746.98 9820.83 6-Nov-03 9820.68 9888.90 9738.53 9856.97 7-Nov-03 9857.12 9945.71 9770.31 9809.79 10-Nov-03 9807.49 9861.05 9702.46 9756.53 11-Nov-03 9756.53 9801.21 9673.64 9737.79 12-Nov-03 9729.50 9882.60 9700.02 9848.83 13-Nov-03 9846.97 9895.71 9740.53 9837.94 14-Nov-03 9836.46 9919.19 9709.13 9768.68 17-Nov-03 9765.64 9775.35 9603.57 9710.83 18-Nov-03 9711.44 9792.16 9601.35 9624.16 19-Nov-03 9620.68 9731.94 9584.31 9690.46 20-Nov-03 9688.46 9756.09 9576.91 9619.42 21-Nov-03 9622.02 9692.53 9556.68 9628.53 24-Nov-03 9629.87 9788.60 9629.87 9747.79 25-Nov-03 9748.68 9821.94 9679.13 9763.94 26-Nov-03 9763.49 9838.01 9689.05 9779.57 28-Nov-03 9779.72 9832.16 9733.20 9782.46 1-Dec-03 9785.35 9943.34 9777.64 9899.05 2-Dec-03 9899.64 9936.97 9798.83 9853.64 3-Dec-03 9851.94 9974.45 9824.31 9873.42 4-Dec-03 9874.83 9978.08 9814.97 9930.82 5-Dec-03 9923.27 9954.16 9819.05 9862.68 8-Dec-03 9862.01 9997.34 9824.83 9965.27 9-Dec-03 9966.45 10048.75 9887.57 9923.42 10-Dec-03 9922.38 10000.53 9848.97 9921.86 11-Dec-03 9922.45 10056.97 9896.16 10008.16 12-Dec-03 10008.75 10091.71 9946.60 10042.16 15-Dec-03 10046.53 10180.97 9994.38 10022.82 16-Dec-03 10023.34 10173.19 9986.23 10129.56 17-Dec-03 10128.75 10186.67 10040.08 10145.26 18-Dec-03 10141.41 10278.82 10117.78 10248.08 19-Dec-03 10249.48 10345.44 10189.63 10278.22 22-Dec-03 10276.48 10371.11 10216.08 10338.00 23-Dec-03 10337.56 10421.48 10265.71 10341.26 24-Dec-03 10341.41 10365.63 10263.04 10305.19 26-Dec-03 10305.85 10368.89 10282.22 10324.67 29-Dec-03 10321.35 10457.78 10319.70 10450.00 30-Dec-03 10449.70 10493.11 10374.52 10425.04 31-Dec-03 10426.30 10494.44 10382.89 10453.92 2-Jan-04 10452.74 10554.96 10367.41 10409.85 5-Jan-04 10411.85 10575.92 10411.85 10544.07 6-Jan-04 10543.85 10584.07 10454.37 10538.66 7-Jan-04 10535.46 10587.55 10432.00 10529.03 8-Jan-04 10530.07 10651.99 10480.59 10592.44 9-Jan-04 10589.25 10603.48 10420.52 10458.89 12-Jan-04 10461.55 10543.03 10389.85 10485.18 13-Jan-04 10485.18 10539.25 10341.19 10427.18 14-Jan-04 10428.67 10573.85 10426.89 10538.37 15-Jan-04 10534.52 10639.03 10454.52 10553.85 16-Jan-04 10556.37 10666.88 10503.70 10600.51 20-Jan-04 10601.40 10676.96 10447.92 10528.66 21-Jan-04 10522.77 10665.70 10453.11 10623.62 22-Jan-04 10624.22 10717.40 10545.03 10623.18 23-Jan-04 10625.25 10691.77 10490.14 10568.29 26-Jan-04 10568.00 10725.18 10510.44 10702.51 27-Jan-04 10701.10 10748.81 10579.33 10609.92 28-Jan-04 10610.07 10703.25 10412.44 10468.37 29-Jan-04 10467.41 10611.56 10369.92 10510.29 30-Jan-04 10510.22 10551.03 10385.56 10488.07 2-Feb-04 10487.78 10614.44 10395.55 10499.18 3-Feb-04 10499.48 10571.48 10414.15 10505.18 4-Feb-04 10503.11 10567.85 10394.81 10470.74 5-Feb-04 10469.33 10566.37 10399.92 10495.55 6-Feb-04 10494.89 10634.81 10433.70 10593.03 9-Feb-04 10592.00 10634.81 10433.70 10579.03 10-Feb-04 10578.74 10667.03 10511.18 10613.85 11-Feb-04 10605.48 10779.40 10561.55 10737.70 12-Feb-04 10735.18 10775.03 10636.44 10694.07 13-Feb-04 10696.22 10755.47 10578.66 10627.85 17-Feb-04 10628.88 10762.07 10628.88 10714.88 18-Feb-04 10706.68 10764.36 10623.62 10671.99 19-Feb-04 10674.59 10794.95 10626.44 10664.73 20-Feb-04 10666.29 10722.77 10559.11 10619.03 23-Feb-04 10619.55 10711.84 10508.89 10609.62 24-Feb-04 10609.55 10681.40 10479.33 10566.37 25-Feb-04 10566.59 10660.73 10509.40 10601.62 26-Feb-04 10598.14 10652.96 10493.70 10580.14 27-Feb-04 10581.55 10689.55 10519.03 10583.92 1-Mar-04 10582.25 10720.14 10568.74 10678.14 2-Mar-04 10678.36 10713.92 10539.40 10591.48 3-Mar-04 10588.59 10651.03 10506.66 10593.11 4-Mar-04 10593.48 10645.33 10522.59 10588.00 5-Mar-04 10582.59 10681.40 10497.11 10595.55 8-Mar-04 10595.37 10677.85 10505.85 10529.48 9-Mar-04 10529.52 10567.03 10391.48 10456.96 10-Mar-04 10457.59 10523.11 10259.34 10296.89 11-Mar-04 10288.85 10356.22 10102.75 10128.38 12-Mar-04 10130.67 10281.63 10097.04 10240.08 15-Mar-04 10238.45 10252.68 10066.08 10102.89 16-Mar-04 10103.41 10253.26 10085.34 10184.67 17-Mar-04 10184.30 10356.59 10184.30 10300.30 18-Mar-04 10298.96 10355.04 10187.78 10295.78 19-Mar-04 10295.85 10355.41 10163.71 10186.60 22-Mar-04 10185.93 10185.93 9985.19 10064.75 23-Mar-04 10066.67 10177.04 10020.75 10063.64 24-Mar-04 10065.41 10140.23 9975.86 10048.23 25-Mar-04 10049.56 10246.15 10049.56 10218.82 26-Mar-04 10218.37 10306.22 10145.63 10212.97 29-Mar-04 10212.91 10389.93 10212.91 10329.63 30-Mar-04 10327.63 10411.41 10264.15 10381.70 31-Mar-04 10380.89 10428.59 10287.11 10357.70 1-Apr-04 10357.52 10449.33 10299.48 10373.33 2-Apr-04 10375.33 10548.74 10375.33 10470.59 5-Apr-04 10470.59 10582.22 10423.33 10558.37 6-Apr-04 10553.76 10596.37 10467.26 10570.81 7-Apr-04 10569.26 10580.51 10422.74 10480.15 8-Apr-04 10482.77 10590.15 10383.84 10442.03 12-Apr-04 10444.38 10559.28 10439.27 10515.56 13-Apr-04 10516.05 10572.13 10343.17 10381.28 14-Apr-04 10378.10 10453.39 10259.35 10377.95 15-Apr-04 10377.95 10481.21 10279.37 10397.46 16-Apr-04 10398.32 10500.57 10343.74 10451.97 19-Apr-04 10451.62 10501.79 10351.97 10437.85 20-Apr-04 10437.85 10530.61 10297.39 10314.50 21-Apr-04 10311.87 10398.53 10200.38 10317.27 22-Apr-04 10314.99 10529.12 10255.88 10461.20 23-Apr-04 10463.11 10543.95 10362.97 10472.84 26-Apr-04 10472.91 10540.26 10396.75 10444.73 27-Apr-04 10445.38 10570.92 10410.52 10478.16 28-Apr-04 10476.67 10479.58 10301.65 10342.60 29-Apr-04 10339.41 10443.81 10199.31 10272.27 30-Apr-04 10273.06 10374.61 10198.39 10225.57 3-May-04 10227.27 10365.74 10199.67 10314.00 4-May-04 10314.32 10403.14 10232.31 10317.20 5-May-04 10316.98 10382.98 10249.63 10310.95 6-May-04 10308.20 10332.10 10147.21 10241.26 7-May-04 10240.62 10302.93 10086.94 10117.34 10-May-04 10116.28 10116.28 9881.86 9990.02 11-May-04 9989.24 10092.78 9928.91 10019.47 12-May-04 10011.52 10089.87 9822.10 10045.16 13-May-04 10044.31 10100.24 9924.94 10010.74 14-May-04 10008.43 10096.69 9912.45 10012.87 17-May-04 10009.92 10009.92 9827.21 9906.91 18-May-04 9906.71 10028.27 9895.77 9968.51 19-May-04 9962.55 10124.79 9919.90 9937.71 20-May-04 9939.12 10014.50 9867.73 9937.64 21-May-04 9939.34 10058.50 9910.81 9966.74 24-May-04 9968.02 10084.91 9891.22 9958.43 25-May-04 9958.08 10139.27 9895.41 10117.62 26-May-04 10116.84 10175.75 10034.16 10109.89 27-May-04 10109.89 10267.66 10106.13 10205.20 28-May-04 10205.83 10250.27 10137.14 10188.45 1-Jun-04 10187.18 10254.17 10104.07 10202.65 2-Jun-04 10199.78 10310.10 10170.57 10262.97 3-Jun-04 10261.85 10309.46 10163.40 10195.91 4-Jun-04 10196.83 10327.84 10196.83 10242.82 7-Jun-04 10243.31 10410.81 10243.31 10391.08 8-Jun-04 10389.41 10462.97 10323.94 10432.52 9-Jun-04 10431.10 10466.59 10325.07 10368.44 10-Jun-04 10367.80 10448.00 10333.94 10410.10 14-Jun-04 10401.23 10403.50 10283.48 10334.73 15-Jun-04 10336.51 10464.04 10319.89 10380.43 16-Jun-04 10380.23 10433.52 10320.60 10379.58 17-Jun-04 10378.59 10417.69 10308.25 10377.52 18-Jun-04 10375.82 10471.84 10328.20 10416.41 21-Jun-04 10417.82 10471.76 10336.44 10371.47 22-Jun-04 10370.21 10431.05 10284.24 10395.07 23-Jun-04 10395.14 10498.67 10323.32 10479.57 24-Jun-04 10477.43 10530.01 10398.16 10443.81 25-Jun-04 10444.24 10514.67 10329.88 10371.84 28-Jun-04 10377.52 10505.16 10317.64 10357.09 29-Jun-04 10356.35 10460.25 10315.65 10413.43 30-Jun-04 10413.43 10489.16 10348.98 10435.48 1-Jul-04 10434.00 10473.23 10255.55 10334.16 2-Jul-04 10334.00 10371.40 10228.71 10282.83 6-Jul-04 10280.26 10308.43 10163.60 10219.34 7-Jul-04 10211.92 10300.53 10156.45 10240.29 8-Jul-04 10238.52 10297.73 10134.99 10171.56 9-Jul-04 10173.12 10277.16 10150.32 10213.22 12-Jul-04 10211.75 10284.39 10130.42 10238.22 13-Jul-04 10238.37 10297.58 10188.45 10247.59 14-Jul-04 10232.84 10313.95 10129.31 10208.80 15-Jul-04 10208.20 10275.27 10115.81 10163.16 16-Jul-04 10162.34 10289.40 10095.32 10139.78 19-Jul-04 10140.95 10211.60 10027.33 10094.06 20-Jul-04 10094.43 10186.90 10031.24 10149.07 21-Jul-04 10156.30 10279.96 10027.92 10046.13 22-Jul-04 10047.60 10114.41 9906.62 10050.33 23-Jul-04 10045.46 10069.51 9893.93 9962.22 26-Jul-04 9964.71 10054.32 9874.38 9961.92 27-Jul-04 9963.54 10133.95 9942.75 10085.14 28-Jul-04 10084.03 10170.31 9966.34 10117.07 29-Jul-04 10115.52 10213.08 10049.74 10129.24 30-Jul-04 10129.12 10194.13 10045.76 10139.71 2-Aug-04 10138.45 10224.29 10063.75 10179.16 3-Aug-04 10178.27 10228.49 10064.57 10120.24 4-Aug-04 10117.96 10186.16 10029.02 10126.51 5-Aug-04 10127.10 10158.44 9945.84 9963.03 6-Aug-04 9960.67 9963.47 9767.54 9815.33 9-Aug-04 9816.14 9902.49 9773.74 9814.66 10-Aug-04 9815.55 9961.70 9798.44 9944.67 11-Aug-04 9931.24 9981.61 9804.63 9938.32 12-Aug-04 9936.48 9940.02 9780.52 9814.59 13-Aug-04 9814.11 9897.34 9746.60 9825.35 16-Aug-04 9825.35 9987.58 9807.44 9954.55 17-Aug-04 9955.50 10053.21 9916.05 9972.83 18-Aug-04 9964.22 10097.01 9910.82 10083.15 19-Aug-04 10082.78 10111.91 9972.39 10040.82 20-Aug-04 10040.81 10143.76 9989.65 10110.14 23-Aug-04 10111.10 10159.54 10046.72 10073.05 24-Aug-04 10074.89 10165.07 10044.66 10098.63 25-Aug-04 10098.49 10224.29 10041.93 10181.74 26-Aug-04 10181.07 10225.61 10124.88 10173.41 27-Aug-04 10174.07 10235.49 10143.91 10195.01 30-Aug-04 10193.83 10226.87 10110.43 10122.52 31-Aug-04 10121.97 10198.03 10056.09 10173.92 1-Sep-04 10170.12 10230.48 10092.37 10168.46 2-Sep-04 10168.39 10312.99 10129.01 10290.28 3-Sep-04 10277.82 10346.99 10229.52 10260.20 7-Sep-04 10261.52 10388.95 10255.62 10341.16 8-Sep-04 10342.42 10390.64 10267.94 10313.36 9-Sep-04 10313.36 10337.33 10269.49 10289.10 10-Sep-04 10289.47 10348.68 10196.19 10313.07 13-Sep-04 10306.65 10380.47 10250.61 10314.76 14-Sep-04 10315.13 10374.79 10260.93 10318.16 15-Sep-04 10316.90 10324.87 10195.60 10231.36 16-Sep-04 10231.59 10315.72 10194.35 10244.49 17-Sep-04 10245.82 10352.37 10219.71 10284.46 20-Sep-04 10283.87 10293.23 10152.90 10204.89 21-Sep-04 10204.52 10291.39 10159.54 10244.93 22-Sep-04 10244.05 10244.05 10075.33 10109.18 23-Sep-04 10108.29 10134.84 9999.67 10038.90 24-Sep-04 10039.42 10111.39 9993.92 10047.24 27-Sep-04 10046.65 10077.32 9952.78 9988.54 28-Sep-04 9989.73 10132.04 9950.71 10077.40 29-Sep-04 10078.06 10160.50 10002.57 10136.24 30-Sep-04 10136.38 10155.49 9987.36 10080.27 1-Oct-04 10082.04 10237.05 10081.38 10192.65 4-Oct-04 10191.40 10313.81 10153.79 10216.54 5-Oct-04 10216.76 10253.93 10123.19 10177.68 6-Oct-04 10170.70 10267.14 10112.20 10239.92 7-Oct-04 10239.84 10267.57 10086.83 10125.40 8-Oct-04 10124.11 10177.53 10013.91 10055.20 11-Oct-04 10056.09 10142.74 10017.67 10081.97 12-Oct-04 10080.42 10121.49 9985.44 10077.18 13-Oct-04 10085.21 10157.11 9935.08 10002.33 14-Oct-04 10002.54 10048.48 9837.22 9894.45 15-Oct-04 9895.63 10022.31 9845.56 9933.38
Explanation / Answer
Moving average of span 3 using minitab
Moving Average for C5
Data C5
Length 253
NMissing 0
Moving Average
Length 3
Accuracy Measures
MAPE 0.66
MAD 67.11
MSD 7166.28
Forecasts
Period Forecast Lower Upper
254 9943.39 9777.47 10109.3
Moving average of span 10
Moving Average for C5
Data C5
Length 253
NMissing 0
Moving Average
Length 10
Accuracy Measures
MAPE 1.1
MAD 110.7
MSD 17615.7
Forecasts
Period Forecast Lower Upper
254 10080.4 9820.27 10340.5
Moving average of span 15
Moving Average for C5
Data C5
Length 253
NMissing 0
Moving Average
Length 15
Accuracy Measures
MAPE 1.3
MAD 131.1
MSD 25314.1
Forecasts
Period Forecast Lower Upper
254 10085.3 9773.44 10397.1
The forecast goes on increases as span increases as smaller the duration more sensitive the forecast is and as the duration increases the data is more smoothen and is less sensitive
