Homework Sourse5 a Given the following time series trend and seasonal index
| 5. | |||||||||||
| a. Given the following time series, trend, and seasonal index, calculate a (recomposed) seasonal forecast for March 2011. | |||||||||||
| b. The October seasonal index is 122.99. Explain how an index value of 122.99 influences the shape of a graph | |||||||||||
| of the forecast curve. | |||||||||||
| Series | Trend | ||||||||||
| Jan 2007 | 1.71 | 3.623 | |||||||||
| Feb | 1.92 | 3.612 | Seasonal Index | ||||||||
| Mar | 3.58 | 3.601 | Jan | 55.91 | |||||||
| Apr | 4.4 | 3.590 | Feb | 63.08 | |||||||
| May | 3.79 | 3.579 | Mar | 85.74 | |||||||
| Jun | 5.52 | 3.568 | Apr | 97.11 | |||||||
| Jul | 5.5 | 3.556 | May | 107.58 | |||||||
| Aug | 5 | 3.545 | Jun | 105.69 | |||||||
| Sep | 5.48 | 3.534 | Jul | 144.87 | |||||||
| Oct | 4.81 | 3.523 | Aug | 145.83 | |||||||
| Nov | 2.42 | 3.512 | Sep | 133.32 | |||||||
| Dec | 1.46 | 3.501 | Oct | 122.99 | |||||||
| Jan 2008 | 1.71 | 3.490 | Nov | 83.23 | |||||||
| Feb | 2.46 | 3.479 | Dec | 54.64 | |||||||
| Mar | 2.42 | 3.468 | |||||||||
| Apr | 1.79 | 3.457 | |||||||||
| May | 3.63 | 3.445 | |||||||||
| Jun | 3.54 | 3.434 | |||||||||
| Jul | 4.88 | 3.423 | |||||||||
| Aug | 4.96 | 3.412 | |||||||||
| Sep | 3.63 | 3.401 | |||||||||
| Oct | 5.46 | 3.390 | |||||||||
| Nov | 3.08 | 3.379 | |||||||||
| Dec | 1.75 | 3.368 | |||||||||
| Jan 2009 | 2.13 | 3.357 | |||||||||
| Feb | 2.58 | 3.346 | |||||||||
| Mar | 2.75 | 3.334 | |||||||||
| Apr | 3.15 | 3.323 | |||||||||
| May | 3.46 | 3.312 | |||||||||
| Jun | 3.33 | 3.301 | |||||||||
| Jul | 4.67 | 3.290 | |||||||||
| Aug | 4.13 | 3.279 | |||||||||
| Sep | 4.73 | 3.268 | |||||||||
| Oct | 3.42 | 3.257 | |||||||||
| Nov | 3.08 | 3.246 | |||||||||
| Dec | 1.79 | 3.235 | |||||||||
| Jan 2010 | 1.96 | 3.223 | |||||||||
| Feb | 1.63 | 3.212 | |||||||||
| Mar | 2.75 | 3.201 | |||||||||
| Apr | 3.06 | 3.190 | |||||||||
| May | 4.31 | 3.179 | |||||||||
| Jun | 3.31 | 3.168 | |||||||||
| Jul | 3.71 | 3.157 | |||||||||
| Aug | 5.25 | 3.146 | |||||||||
| Sep | 3.67 | 3.135 | |||||||||
| Oct | 3.1 | 3.124 | |||||||||
| Nov | 2.25 | 3.112 | |||||||||
| Dec | 2.29 | 3.101 | |||||||||
| Jan 2011 | 3.090 | ||||||||||
| Feb | 3.079 | ||||||||||
| Mar | 3.068 | ||||||||||
| Apr | 3.057 | ||||||||||
| May | 3.046 | ||||||||||
| Jun | 3.035 | ||||||||||
| Jul | 3.024 | ||||||||||
| Aug | 3.013 | ||||||||||
| Sep | 3.001 | ||||||||||
| Oct | 2.990 | ||||||||||
| Nov | 2.979 | ||||||||||
| Dec | 2.968 | ||||||||||
| 5. | |||||||||||
| a. Given the following time series, trend, and seasonal index, calculate a (recomposed) seasonal forecast for March 2011. | |||||||||||
| b. The October seasonal index is 122.99. Explain how an index value of 122.99 influences the shape of a graph | |||||||||||
| of the forecast curve. | |||||||||||
| Series | Trend | ||||||||||
| Jan 2007 | 1.71 | 3.623 | |||||||||
| Feb | 1.92 | 3.612 | Seasonal Index | ||||||||
| Mar | 3.58 | 3.601 | Jan | 55.91 | |||||||
| Apr | 4.4 | 3.590 | Feb | 63.08 | |||||||
| May | 3.79 | 3.579 | Mar | 85.74 | |||||||
| Jun | 5.52 | 3.568 | Apr | 97.11 | |||||||
| Jul | 5.5 | 3.556 | May | 107.58 | |||||||
| Aug | 5 | 3.545 | Jun | 105.69 | |||||||
| Sep | 5.48 | 3.534 | Jul | 144.87 | |||||||
| Oct | 4.81 | 3.523 | Aug | 145.83 | |||||||
| Nov | 2.42 | 3.512 | Sep | 133.32 | |||||||
| Dec | 1.46 | 3.501 | Oct | 122.99 | |||||||
| Jan 2008 | 1.71 | 3.490 | Nov | 83.23 | |||||||
| Feb | 2.46 | 3.479 | Dec | 54.64 | |||||||
| Mar | 2.42 | 3.468 | |||||||||
| Apr | 1.79 | 3.457 | |||||||||
| May | 3.63 | 3.445 | |||||||||
| Jun | 3.54 | 3.434 | |||||||||
| Jul | 4.88 | 3.423 | |||||||||
| Aug | 4.96 | 3.412 | |||||||||
| Sep | 3.63 | 3.401 | |||||||||
| Oct | 5.46 | 3.390 | |||||||||
| Nov | 3.08 | 3.379 | |||||||||
| Dec | 1.75 | 3.368 | |||||||||
| Jan 2009 | 2.13 | 3.357 | |||||||||
| Feb | 2.58 | 3.346 | |||||||||
| Mar | 2.75 | 3.334 | |||||||||
| Apr | 3.15 | 3.323 | |||||||||
| May | 3.46 | 3.312 | |||||||||
| Jun | 3.33 | 3.301 | |||||||||
| Jul | 4.67 | 3.290 | |||||||||
| Aug | 4.13 | 3.279 | |||||||||
| Sep | 4.73 | 3.268 | |||||||||
| Oct | 3.42 | 3.257 | |||||||||
| Nov | 3.08 | 3.246 | |||||||||
| Dec | 1.79 | 3.235 | |||||||||
| Jan 2010 | 1.96 | 3.223 | |||||||||
| Feb | 1.63 | 3.212 | |||||||||
| Mar | 2.75 | 3.201 | |||||||||
| Apr | 3.06 | 3.190 | |||||||||
| May | 4.31 | 3.179 | |||||||||
| Jun | 3.31 | 3.168 | |||||||||
| Jul | 3.71 | 3.157 | |||||||||
| Aug | 5.25 | 3.146 | |||||||||
| Sep | 3.67 | 3.135 | |||||||||
| Oct | 3.1 | 3.124 | |||||||||
| Nov | 2.25 | 3.112 | |||||||||
| Dec | 2.29 | 3.101 | |||||||||
| Jan 2011 | 3.090 | ||||||||||
| Feb | 3.079 | ||||||||||
| Mar | 3.068 | ||||||||||
| Apr | 3.057 | ||||||||||
| May | 3.046 | ||||||||||
| Jun | 3.035 | ||||||||||
| Jul | 3.024 | ||||||||||
| Aug | 3.013 | ||||||||||
| Sep | 3.001 | ||||||||||
| Oct | 2.990 | ||||||||||
| Nov | 2.979 | ||||||||||
| Dec | 2.968 | ||||||||||
Solution
let us discuss what is seasonal index,
A forecasting tool used to determine demand for various commodities or goods in a given marketplace over the course of a typical year (or a shorter time period). Such an index is based on data from previous years that highlights seasonal differences in consumption. In some industries, the seasonality index experiences huge swings. For example, toy makers are likely to experience peak demand in the month leading up to Christmas. Data from a seasonality index may be used to determine safety lead times or safety stock levels.
in our problem the seosonal index for oct is 122.99, which 4th highest index in the year. the 1st 3 are 144.87, 145.85, 133.32 for the month jul. aug,sep. so we can comment that the sale is 4th highest in the month october.
