Let
be the
th value of a time series
, for
after non-seasonal differencing of order
and seasonal differencing of order
(with period or seasonality
). In general,
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Non-seasonal differencing up to the required order
is obtained using
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for |
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for |
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for |
Seasonal differencing up to the required order
is then obtained using
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for |
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for |
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for |
Mathematically, the sequence in which the differencing operations are performed does not affect the final resulting series of values.
None.
The computations are believed to be stable.
Background information to multithreading can be found in the
Multithreading documentation.