I'm dealing with time series data about sales in a supermarket.

When I fit the model using auto.arima(data), I don't get any seasonal component (weekly) and if I impose a seasonal component I get 'no arima suitable model was found'.

Then I fitted a new model, ARIMAX, using 6 day of week regressors( I omitted one to avoid collinearity) and I found them significative by calculating the p value (being the coefficients MLE estimates they are asimptotically normal).

Am I missing a conceptual difference between these 2 models??


You might review How to model timeseries with unequally-spaced seasonality interval noting that the data that was analyzed there was only for 365 days thus no holiday effects or weekly effects or monthly effects etc. were available to be identified. The problem you are facing is not amenable by either of your two approaches as what you need is a hybrid model that not only incorporates known events including possible price/promotion effects but memory as needed (ARIMA structure) while dealing with anomalies and possible level shifts and trends. One needs to deal with this data in a holistic manner as piecemeal approaches as you were trying will be (normally/always) insufficient.

The arima attempt that you were trying only uses memory while the fixed days attempt is deterministic only in form. One needs to optimally combine both kinds of components while incorporating possible user suggested "causal/predictor/exogenous/helping/supporting" series.


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