In: Economics
The following table reports the Consumer Pirce Index for the Los Angeles area on a monthly basis from January 1998 to December 2000 (base year=1982-1984). Eliminating the data for 2000, use Excel to forecast the index for all of 2000 using a three-and -six month average. Which provides a better forecast for 2000 using the data provided?
Salvatore Chapter 6 Appendix Problem 3 (p.261) | |||||
Time | CPI | forecast(w=0.3) | (A-F)^2 | forecast(w=0.7) | (A-F)^2 |
Jan-98 | 161.0 | 166.63 | 166.63 | ||
Feb-98 | 161.1 | 164.94 | |||
Mar-98 | 161.4 | 163.79 | |||
Apr-98 | 161.8 | 163.07 | |||
May-98 | 162.3 | 162.69 | |||
Jun-98 | 162.2 | 162.57 | |||
Jul-98 | 162.1 | 162.46 | |||
Aug-98 | 162.6 | 162.35 | |||
Sep-98 | 162.6 | 162.43 | |||
Oct-98 | 163.2 | 162.48 | |||
Nov-98 | 163.4 | 162.70 | |||
Dec-98 | 163.5 | 162.91 | |||
Jan-99 | 164.2 | 163.08 | |||
Feb-99 | 164.6 | 163.42 | |||
Mar-99 | 165.0 | 163.77 | |||
Apr-99 | 166.6 | 164.14 | |||
May-99 | 166.2 | 164.88 | |||
Jun-99 | 165.4 | 165.28 | |||
Jul-99 | 165.8 | 165.31 | |||
Aug-99 | 166.3 | 165.46 | |||
Sep-99 | 167.2 | 165.71 | |||
Oct-99 | 167.2 | 166.16 | |||
Nov-99 | 167.1 | 166.47 | |||
Dec-99 | 167.3 | 166.66 | |||
Jan-00 | 167.9 | 166.85 | 1.10 | ||
Feb-00 | 169.3 | 167.17 | 4.55 | ||
Mar-00 | 170.7 | 167.81 | 8.37 | ||
Apr-00 | 170.6 | 168.67 | 3.71 | ||
May-00 | 171.1 | 169.25 | 3.41 | ||
Jun-00 | 171.0 | 169.81 | 1.42 | ||
Jul-00 | 171.7 | 170.16 | 2.36 | ||
Aug-00 | 172.2 | 170.63 | 2.48 | ||
Sep-00 | 173.3 | 171.10 | 4.85 | ||
Oct-00 | 173.8 | 171.76 | 4.17 | ||
Nov-00 | 173.5 | 172.37 | 1.28 | ||
Dec-00 | 173.5 | 172.71 | 0.62 |
Time | CPI | 3-Month Moving Average | 6-Month Moving Average | Error for 3-M MA | Absolute Error for 3-M MA | Error for 6-M MA | Absolute Error for 6-M MA |
Jan-98 | 161 | ||||||
Feb-98 | 161.1 | ||||||
Mar-98 | 161.4 | ||||||
Apr-98 | 161.8 | ||||||
May-98 | 162.3 | ||||||
Jun-98 | 162.2 | ||||||
Jul-98 | 162.1 | ||||||
Aug-98 | 162.6 | ||||||
Sep-98 | 162.6 | ||||||
Oct-98 | 163.2 | ||||||
Nov-98 | 163.4 | ||||||
Dec-98 | 163.5 | ||||||
Jan-99 | 164.2 | ||||||
Feb-99 | 164.6 | ||||||
Mar-99 | 165 | ||||||
Apr-99 | 166.6 | ||||||
May-99 | 166.2 | ||||||
Jun-99 | 165.4 | ||||||
Jul-99 | 165.8 | ||||||
Aug-99 | 166.3 | ||||||
Sep-99 | 167.2 | ||||||
Oct-99 | 167.2 | ||||||
Nov-99 | 167.1 | ||||||
Dec-99 | 167.3 | ||||||
Jan-00 | 167.9 | 167.2 | 166.8 | 0.7 | 0.7 | 1.1 | 1.1 |
Feb-00 | 169.3 | 167.4 | 167.2 | 1.9 | 1.9 | 2.1 | 2.1 |
Mar-00 | 170.7 | 168.2 | 167.7 | 2.5 | 2.5 | 3.0 | 3.0 |
Apr-00 | 170.6 | 169.3 | 168.3 | 1.3 | 1.3 | 2.3 | 2.3 |
May-00 | 171.1 | 170.2 | 168.8 | 0.9 | 0.9 | 2.3 | 2.3 |
Jun-00 | 171 | 170.8 | 169.5 | 0.2 | 0.2 | 1.5 | 1.5 |
Jul-00 | 171.7 | 170.9 | 170.1 | 0.8 | 0.8 | 1.6 | 1.6 |
Aug-00 | 172.2 | 171.3 | 170.7 | 0.9 | 0.9 | 1.5 | 1.5 |
Sep-00 | 173.3 | 171.6 | 171.2 | 1.7 | 1.7 | 2.1 | 2.1 |
Oct-00 | 173.8 | 172.4 | 171.7 | 1.4 | 1.4 | 2.2 | 2.2 |
Nov-00 | 173.5 | 173.1 | 172.2 | 0.4 | 0.4 | 1.3 | 1.3 |
Dec-00 | 173.5 | 173.5 | 172.6 | 0.0 | 0.0 | 0.9 | 0.9 |
MAD for 3 month moving average = (sum of the absolute errors)/no. of observation | |||||||
MAD for 3 month moving average = (.7+1.9+2.5+1.3+.9+.2+.8+.9+1.7+1.4+.4+0)/10 | |||||||
MAD for 3 month moving average = 1.27 | |||||||
MAD for 6 month moving average = (sum of the absolute errors)/no. of observation | |||||||
MAD for 6 month moving average = (1.1+2.1+3.0+2.3+2.3+1.5+1.6+1.5+2.1+2.2+1.3+.9)/10 | |||||||
MAD for 6 month moving average = 2.19 |
Since MAD is greater for the 6 month moving average, than the 3 month moving average, then it is good to go with the 3 month moving average that represents superior accuracy in the forecast.