The problem

Daily sales at a grocery chain follow a strong weekly rhythm, but promotions and holidays throw spikes at it that a naive forecast can’t see coming. Baseline forecasts either ignore the weekly seasonality entirely or get blindsided by holiday demand.

Approach

A SARIMAX pipeline on the Store Sales dataset (GROCERY I at a single store, ~4.5 years of daily sales):

  • Log transform + seasonal differencing — log1p for variance stabilisation, d=1, D=1, s=7 established via ACF/PACF and the ADF test
  • Exogenous regressor — the onpromotion flag fed into the model via exog
  • Back-transformation — expm1 to invert log1p, clipped at zero so confidence intervals never go negative
  • Residual diagnostics — residuals over time and histogram checked right after fitting, before trusting any forecast
  • Scoring — MAE / RMSE / MAPE / NRMSE computed on the real sales scale against a 60-day holdout

Result

A working end-to-end notebook: forecast with 95% confidence interval plotted against test actuals, scored on the real sales scale, with residual diagnostics to sanity-check the model. The walkthrough is written up as an essay, and the runnable notebook is available to download: