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:: Standard Deviation-Mean Plot :: |
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Server date: May 18, 2008, 3:00 am
Note: these SMP calculations are always applied to the untransformed and undifferenced (original) time series.
| SMP of Airline.ds |
| L = 1, d = D = 0 |
| Section | Mean(k) | SE(k) |
| 1 | 126.6667 | 13.7201 |
| 2 | 139.6667 | 19.0708 |
| 3 | 170.1667 | 18.4383 |
| 4 | 197 | 22.9664 |
| 5 | 225 | 28.4669 |
| 6 | 238.9167 | 34.9245 |
| 7 | 284 | 42.1405 |
| 8 | 328.25 | 47.8618 |
| 9 | 368.4167 | 57.8909 |
| 10 | 381 | 64.5305 |
| 11 | 428.3333 | 69.8301 |
| 12 | 476.1667 | 77.7371 |
| Regression: S.E.(k) = alpha + beta * Mean(k) |
| alpha | -11.403254142558 |
| beta | 0.18861339889948 |
| S.E. | 0.0065773318024468 |
| T-Stat | 28.676278552546 |
| The above regression result suggests that a relationship exists between the mean level and the standard error of this time series. |
| Regression: ln S.E.(k) = -3.7070398932205 + 1.3125925397258 * ln Mean(k) |
| alpha | -3.7070398932205 |
| beta | 1.3125925397258 |
| S.E. | 0.054820180413853 |
| T-Stat | 23.943601239847 |
| Lambda | -0.31259253972575 |
| AI Conclusion: A Box-Cox transform is likely to induce stationarity of variance. |
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From this analysis it can be concluded that the time series under investigation should be transformed according to the Box-Cox transformation with lambda = -0.31. For the sake of convenience we apply lambda = 0. |
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Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
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