A Meta-Model for Fashion Retail Category Sales Forecasting

Abstract

Companies working in fashion retail require scientific methods to transform the enormous amounts of data they collect into information that can be useful to predict future sales. Literature has presented a huge number of statistical/data-science based techniques, able to perform forecasting of time series, like the number of pieces—belonging to a certain brand or category—sold in retail stores. This paper aims to put together some of these methods to build a robust meta-model able to better understand the hidden relationships between data. Classical and more recent methods to compute a category level forecast are shown, giving particular attention to the modeling of price effect. Finally, we show that the use of a metamodel helps reducing the forecasting error on the yearly category forecast by 24%.

Appendix: Main Forecast Error Measurements

Observed value of the i-th time series at time t: $Y_{i,t}$.

Predicted value of the i-th time series at time t: $F_{i,t}$ .

Error of the single observation: $e_{i,t} = Y_{i,t} - F_{i,t}$.

Mean absolute error: $MAE_i=\sum _{t} |e_{i,t}|/n_i$. Scale dependent.

Percentage error: $p_{i,t}=(Y_{i,t}-F_{i,t})/Y_{i,t}$. Requires $Y_{i,t}\ne 0$.

Mean absolute percentage error: $MAPE_i=\sum _{t} |p_{i,t}|/n_i$. Sensitive to $Y_{i,t}\approx 0$.

Relative error between forecasts $F_{i,t}$ and $F_{i,t}^b$ (benchmark): $RE_{i,t}=e_{i,t}/e^b_{i,t}$.

Benchmark-scaled error: $q_{i,t}=e_{i,t}/MAE_i^b$.

Mean absolute scaled error: $r_i=\sum _{t} |q_{i,t}|/n_i= MAE_i/MAE^b_i$.

Average Relative MAE: $AvgRelMAE= \Big (\prod \nolimits _{i=1}^m r_i^{n_i}\Big )^{\frac{1}{\sum _{i=1}^m n_i}}$. Geometric mean of MAEs.

$AvgRelMAE<1 \Leftrightarrow MAE^a_i < MAE^b_i \Leftrightarrow$ Model A is more accurate than model B.