A seasonal series with noiseThe classical decomposition expressed the time series { X t } as a sum…

A seasonal series with noise

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The classical decomposition expressed the time series {Xt} as a sum of trend, seasonal, and noise components. The seasonal component (with period d) was a sequence {st} with the properties st+dstand

 width= Such a sequence can be generated, for any values of s1, s0, . . . , sd+3, by means of the recursions

st+1 = −st −· · ·−std+2, t= 12, . . . .

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