Homework Soursethe unemployment rates provides data on monthly rates for 4
the unemployment rates provides data on monthly rates for 4 years. Compare 3- and 12- month moving average forecasts using the MAD criterion. explain why the 3 month model yields better results
| Unemployment Rates | ||
| Year | Month | Rate (%) |
| 2009 | Jan | 7.8 |
| 2009 | Feb | 8.3 |
| 2009 | Mar | 8.7 |
| 2009 | Apr | 9.0 |
| 2009 | May | 9.4 |
| 2009 | Jun | 9.5 |
| 2009 | Jul | 9.5 |
| 2009 | Aug | 9.6 |
| 2009 | Sep | 9.8 |
| 2009 | Oct | 10.0 |
| 2009 | Nov | 9.9 |
| 2009 | Dec | 9.9 |
| 2010 | Jan | 9.8 |
| 2010 | Feb | 9.8 |
| 2010 | Mar | 9.9 |
| 2010 | Apr | 9.9 |
| 2010 | May | 9.6 |
| 2010 | Jun | 9.4 |
| 2010 | Jul | 9.5 |
| 2010 | Aug | 9.5 |
| 2010 | Sep | 9.5 |
| 2010 | Oct | 9.5 |
| 2010 | Nov | 9.8 |
| 2010 | Dec | 9.3 |
| 2011 | Jan | 9.1 |
| 2011 | Feb | 9.0 |
| 2011 | Mar | 8.9 |
| 2011 | Apr | 9.0 |
| 2011 | May | 9.0 |
| 2011 | Jun | 9.1 |
| 2011 | Jul | 9.0 |
| 2011 | Aug | 9.0 |
| 2011 | Sep | 9.0 |
| 2011 | Oct | 8.9 |
| 2011 | Nov | 8.6 |
| 2011 | Dec | 8.5 |
| 2012 | Jan | 8.3 |
| 2012 | Feb | 8.3 |
| 2012 | Mar | 8.2 |
| 2012 | Apr | 8.1 |
| 2012 | May | 8.2 |
| 2012 | Jun | 8.2 |
| 2012 | Jul | 8.2 |
| 2012 | Aug | 8.1 |
| 2012 | Sep | 7.8 |
| 2012 | Oct | 7.9 |
| 2012 | Nov | 7.8 |
| 2012 | Dec | 7.8 |
Solution
Sol)
From Excel
From above analysis
MAD for 3 months=0.0379
for 12 months=0.182
Hence MAD for 3 months is less than for 12 months hence we conclude that 3 months moving average is better thean 12 months
| Rate (%) | 3 month | 12 month | (yi-yhat) for 3 months | (yi-yhat) for 3 months | ||
| 2009 | Jan | 7.8 | ||||
| 2009 | Feb | 8.3 | ||||
| 2009 | Mar | 8.7 | ||||
| 2009 | Apr | 9 | 8.2667 | |||
| 2009 | May | 9.4 | 8.6667 | |||
| 2009 | Jun | 9.5 | 9.0333 | |||
| 2009 | Jul | 9.5 | 9.3 | |||
| 2009 | Aug | 9.6 | 9.4667 | |||
| 2009 | Sep | 9.8 | 9.5333 | |||
| 2009 | Oct | 10 | 9.6333 | |||
| 2009 | Nov | 9.9 | 9.8 | |||
| 2009 | Dec | 9.9 | 9.9 | 9.283333 | 0 | 0.62 |
| 2010 | Jan | 9.8 | 9.9333 | 9.45 | -0.13 | 0.35 |
| 2010 | Feb | 9.8 | 9.8667 | 9.575 | -0.07 | 0.23 |
| 2010 | Mar | 9.9 | 9.8333 | 9.675 | 0.07 | 0.23 |
| 2010 | Apr | 9.9 | 9.8633 | 9.75 | 0.04 | 0.15 |
| 2010 | May | 9.6 | 9.7967 | 9.766667 | -0.20 | -0.17 |
| 2010 | Jun | 9.4 | 9.6633 | 9.758333 | -0.26 | -0.36 |
| 2010 | Jul | 9.5 | 9.5 | 9.758333 | 0.00 | -0.26 |
| 2010 | Aug | 9.5 | 9.4667 | 9.75 | 0.03 | -0.25 |
| 2010 | Sep | 9.5 | 9.5 | 9.725 | 0.00 | -0.23 |
| 2010 | Oct | 9.5 | 9.5 | 9.683333 | 0.00 | -0.18 |
| 2010 | Nov | 9.8 | 9.6 | 9.675 | 0.20 | 0.13 |
| 2010 | Dec | 9.3 | 9.5333 | 9.625 | -0.23 | -0.32 |
| 2011 | Jan | 9.1 | 9.4 | 9.566667 | -0.30 | -0.47 |
| 2011 | Feb | 9 | 9.1333 | 9.5 | -0.13 | -0.50 |
| 2011 | Mar | 8.9 | 9 | 9.416667 | -0.10 | -0.52 |
| 2011 | Apr | 9 | 8.9667 | 9.341667 | 0.03 | -0.34 |
| 2011 | May | 9 | 8.9667 | 9.291667 | 0.03 | -0.29 |
| 2011 | Jun | 9.1 | 9.0333 | 9.266667 | 0.07 | -0.17 |
| 2011 | Jul | 9 | 9.0333 | 9.225 | -0.03 | -0.23 |
| 2011 | Aug | 9 | 9.0333 | 9.183333 | -0.03 | -0.18 |
| 2011 | Sep | 9 | 9 | 9.141667 | 0.00 | -0.14 |
| 2011 | Oct | 8.9 | 8.9667 | 9.091667 | -0.07 | -0.19 |
| 2011 | Nov | 8.6 | 8.8333 | 8.991667 | -0.23 | -0.39 |
| 2011 | Dec | 8.5 | 8.6667 | 8.925 | -0.17 | -0.42 |
| 2012 | Jan | 8.3 | 8.4667 | 8.858333 | -0.17 | -0.56 |
| 2012 | Feb | 8.3 | 8.3667 | 8.8 | -0.07 | -0.50 |
| 2012 | Mar | 8.2 | 8.2 | 8.741667 | 0.00 | -0.54 |
| 2012 | Apr | 8.1 | 8.1333 | 8.666667 | -0.03 | -0.57 |
| 2012 | May | 8.2 | 8.1 | 8.6 | 0.10 | -0.40 |
| 2012 | Jun | 8.2 | 8.1667 | 8.525 | 0.03 | -0.33 |
| 2012 | Jul | 8.2 | 8.1333 | 8.458333 | 0.07 | -0.26 |
| 2012 | Aug | 8.1 | 8.1 | 8.383333 | 0.00 | -0.28 |
| 2012 | Sep | 7.8 | 7.9667 | 8.283333 | -0.17 | -0.48 |
| 2012 | Oct | 7.9 | 7.9333 | 8.2 | -0.03 | -0.30 |
| 2012 | Nov | 7.8 | 7.8333 | 8.133333 | -0.03 | -0.33 |
| 2012 | Dec | 7.8 | 7.8333 | 8.075 | -0.03 | -0.27 |
| sum= | -1.82 | -8.74 | ||||
| abosulte | 1.82 | 8.74 | ||||
| Mad | 0.037916667 | 0.182083333 |
