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I am new to ARIMA modeling and currently encountering a weird situation with time series of count data. The time plot shows clear seasonal patterns.ACF also hints on presence of seasonality. However, seasonal unit root test in R shows that series is seasonally stationary.

If I include seasonal differencing (D=1), I cannot find a single model where residuals satisfy normality assumption, even if I perform log- or - square root- or Box-Cox transformations of original series. If I do not include seasonal differencing (keeping seasonal AR and MA parameters is in the model), I easily identify a model with great diagnostics (residuals are white noise and normally distributed).

Having hard time solving the puzzle whether seasonal-looking data can be seasonally stationary. Will appreciate any suggestion.

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  • $\begingroup$ Hello Jane, may I ask you which test you applied? Was it 'nsdiffs' from 'forecast' package? $\endgroup$
    – DatamineR
    Commented Jul 13, 2013 at 10:32

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Well, it's simply that clear seasonal correlations don't always imply that you need seasonal differencing; the seasonal effect can be modelled fine with seasonal moving average & autoregressive terms. It's the same in non-seasonal models; just because you see a strong autocorrelation doesn't necessarily mean you need to difference the series. Sounds like you solved the 'puzzle' by fitting a good model to the undifferenced series that still incorporated seasonal effects.

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  • $\begingroup$ Many thanks Scortchi for your help! Now I am not worried about differencing. $\endgroup$
    – Jane
    Commented Apr 9, 2013 at 14:13

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