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.