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:: Standard Deviation-Mean Plot ::

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Server date: March 23, 2017, 6:09 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
SectionMean(k)SE(k)
1126.666713.7201
2139.666719.0708
3170.166718.4383
419722.9664
522528.4669
6238.916734.9245
728442.1405
8328.2547.8618
9368.416757.8909
1038164.5305
11428.333369.8301
12476.166777.7371


Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.403254142558
beta0.18861339889948
S.E.0.0065773318024468
T-Stat28.676278552546
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
beta1.3125925397258
S.E.0.054820180413853
T-Stat23.943601239847
Lambda-0.31259253972575
AI Conclusion: A Box-Cox transform is likely to induce stationarity of variance.






Regression plot

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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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Algorithms & Software : Patrick Wessa, PhD
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