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why for example seasonal ARIMA(1,0,0)(1,0,0) does not include seasonal differencing. Existence of seasonality imply the need for seasonal differencing? Please explain this corellation. Regards, Nikola

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If you have a model of the form (0,0,0)(1,0,0)12 with coefficient .9999999 this can be rewritten as (0,0,0)(0,1,0)12 and similarly

if you have (1,0,0)(0,0,0,)12 with coefficient .9999999 then you have (0,1,0)(0,0,0)12

the value of .999999 is used to illustrate a coefficient nearly 1

on another note if you need to incorporate seasonal dummies ARIMA gets VERY CONFUSED and attempts to use a seasonal factor OR a seasonal differencing leading to CHAOS (or rather an inefficient/incorrect model). In other words seasonal auto-correlation is a symptom looking for/suggesting a cause.

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