Demand Forecasting in Retail

Core Statistics:

• 42,840 hierarchical time series from Walmart stores
• 1,969 days of daily sales data (January 2011 - June 2016)
• 3,049 individual products across 3 categories and 7 departments
• 10 stores spanning 3 states (California, Texas, Wisconsin)
• Rich contextual data: pricing, calendar events, SNAP eligibility

Hierarchical Structure:

The dataset enables analysis at 12 aggregation levels:

• Total sales (1 series)
• State level (3 series)
• Store level (10 series)
• Category and Department levels
• Product-Store combinations (30,490 series)

Figure: M5 Dataset hierarchical structure showing organization from total sales down to individual product-store combinations

Overall Sales Patterns:

• Clear upward trend with seasonal variations and weekly cyclicality
• Notable sales drops on Christmas Day due to store closures
• Strong annual cyclicality with holiday peaks
• Consistent weekend sales dominance

Figure: Overall sales trends showing clear upward trajectory with seasonal patterns

Geographic Distribution:

• California accounts for ~45% of total sales with notable drops in 2013 and 2015
• Texas shows ~35% of sales with more stable patterns
• Wisconsin exhibits ~20% with significant seasonal variations

Figure: Sales comparison across states showing California's dominance in sales volume

Product Category Performance:

• FOODS category dominates (65% of sales) with consistent weekly seasonality
• HOUSEHOLD (20%) shows strong promotional sensitivity
• HOBBIES (15%) exhibits high seasonality and event-driven spikes

Figure: Product category comparison showing FOODS as the dominant category

Store-Level Analysis:

Figure: Individual store performance showing significant variations within and across states

Department-Level Patterns:

Figure: Sales patterns across departments showing FOODS_3 dominance

Seasonality Analysis:

• Annual peaks: November-December (40-60% sales increase)
• Low periods: January-February post-holiday decline
• Weekend dominance: 20-30% higher sales than weekdays
• State-specific patterns: Wisconsin shows inverted seasonal trends

Annual seasonal patterns

Weekly patterns showing weekend dominance

Figure: State-specific seasonal patterns after trend removal and scaling

Price-Based Features:

• Current selling price and historical statistics (min, max, mean, std)
• Price momentum indicators (weekly, monthly, annual trends)
• Price volatility measures and normalization
• Cross-product price relationships

Temporal Features:

• Calendar features: Day of month, week, month, year, day of week
• Holiday and event markers (religious, cultural, sporting events)
• Weekend indicators and seasonal decomposition

Statistical Features:

• Rolling window statistics: 7, 14, 28-day moving averages
• Lag features: Sales history from 1, 7, 14, 21, 28 days prior
• Exponentially weighted moving averages
• Trend indicators using first differences

1. Linear Regression

Baseline statistical approach using 28-day lag features

• Simple interpretable model for benchmark comparison
• Utilizes engineered features from preprocessing pipeline

2. Exponential Smoothing

Holt-Winters method with additive seasonality

• 7-day seasonal period capturing weekly patterns
• Individual models per product-store combination
• No external features - pure time series approach
• Excellent computational efficiency

3. LightGBM (Three Architectures)

Gradient boosted decision trees at multiple aggregation levels:

• Item-Store Level: Individual models per product-store combination
• Category-Store Level: Multivariate models per category-store (28 models per horizon)
• Store Level: Comprehensive models per store handling all products
• Feature-rich approach incorporating all engineered features

4. LSTM Neural Network

Global deep learning model with advanced architecture:

• 4 hidden layers with 128 neurons each
• 28-day input window predicting next 7 days
• Single model trained on all time series
• MinMax scaling (0-1) applied per time series
• Selected features: price, temporal, and statistical indicators

Random Forest Analysis:

• Price features (mean, std) show highest importance scores
• Temporal index critical for capturing seasonality
• Product variety (item_nunique) impacts store demand significantly
• Price momentum (monthly/yearly trends) highly informative

Figure: Random Forest feature importance showing price and temporal features as key predictors

Mutual Information Analysis:

• Captures non-linear relationships missed by correlation
• All price-related variables show high mutual information
• Different features provide unique complementary information

Figure: Mutual Information analysis highlighting non-linear relationships between features and sales

SHAP Analysis (LightGBM):

• Recent sales history (lag-1) shows highest impact
• Feature significance decreases with temporal distance
• Product-specific characteristics (item_id) contribute substantially
• Multiple features work together for optimal predictions

Figure: SHAP analysis revealing feature contribution patterns for one-step-ahead sales prediction

Overall Model Comparison:

Key Findings:

• LSTM Excellence: Best WRMSSE (0.884) - would rank 11th in M5 competition (only 0.009 points from winner)
• Exponential Smoothing Surprise: Best MAE (1.11) despite simplicity - would achieve 23rd place in M5
• Store-Level LGBM: Best balance among LGBM variants
• Item-Level Challenges: Insufficient data per model led to poor generalization

RMSE Distribution:

• All models show strong concentration of RMSE values in 0-1 range
• LSTM demonstrates most consistent error distribution with lowest outlier counts (267 cases with RMSE > 10)
• LGBM-item exhibits highest maximum RMSE (~120) indicating severe overfitting cases

RMSE distribution across models

BoxPlot revealing model stability

MAE Distribution:

• MAE distributions show smoother patterns than RMSE with reduced outlier impact
• Median performance similar across models, but variance differs significantly
• Less sensitivity to outliers compared to RMSE

MAE distribution patterns

MAE BoxPlot comparison