Feature Engineering for Time Series

Create input variables by shifting the target time series backward by a fixed number of time steps. A lag-7 feature for daily sales captures the value from exactly one week prior, enabling the model to learn weekly seasonality directly. Selecting optimal lags is guided by partial autocorrelation function (PACF) plots, which isolate the direct relationship at each lag after removing intermediary effects. Excessive lag features increase dimensionality and risk overfitting; regularization techniques like Lasso can perform automatic lag selection.

Compute aggregate statistics over a sliding temporal window to capture local trend and volatility. Common transformations include:

• Rolling mean: A 7-day moving average smooths noise and reveals the underlying trend.
• Rolling standard deviation: Quantifies recent demand volatility, critical for dynamic safety stock calculations.
• Rolling min/max: Captures peak and trough behavior within the window.
• Exponentially weighted moving average (EWMA): Applies higher weights to recent observations, making the feature more responsive to sudden shifts than a simple moving average.

Extract deterministic calendar-based features from timestamps to encode recurring patterns. Key decompositions include:

• Day of week (1-7): Captures weekly sales cycles.
• Month of year (1-12): Encodes annual seasonality.
• Day of month: Models payroll cycles and month-end spending spikes.
• Is_holiday (boolean): Flags known high-demand or low-demand periods.
• Sine/cosine cyclical encoding: Transforms cyclical features like month into continuous coordinates sin(2π * month/12) and cos(2π * month/12), preserving the circular distance between December and January for the model.

Engineer features that summarize behavior over fixed historical periods rather than sliding windows. Examples include:

• Sales last 7 days: Total demand in the prior week.
• Sales same day last week: A specific lag for weekly pattern matching.
• Average sales last 4 weeks: A stable baseline for recent demand level.
• Days since last promotion: Encodes recency of a causal event. These features are often pre-computed in a feature store to ensure low-latency retrieval during online inference for real-time demand sensing.

Apply mathematical transformations to the target variable to stabilize variance and make the series more amenable to forecasting models that assume normality. Common transformations:

• Log transform: Reduces the impact of extreme spikes in intermittent or high-variance demand.
• Box-Cox transform: A parametric family of power transformations that optimally normalizes the distribution.
• Differencing: Subtracting the previous observation y(t) - y(t-1) to remove trend and achieve stationarity, a core requirement for ARIMA models. The order of differencing is a critical hyperparameter.

Incorporate exogenous variables that causally influence demand but are not derived from the target's own history. Critical external regressors for retail forecasting include:

• Promotional flags: Binary indicators for price discounts or marketing campaigns.
• Price changes: The percentage or absolute change in product price.
• Weather data: Temperature, precipitation, or severe weather indices that drive demand for seasonal goods.
• Competitor activity: Proxies for competitor stockouts or promotions. These features transform a univariate model into a causal forecasting system, improving accuracy during irregular events.

The foundational technique of creating input variables from past values of the target series. A lag of order k shifts the observation window back by k time steps, allowing models to learn autocorrelation patterns.

• Example: sales_lag_7 represents sales from exactly one week ago.
• Use Case: Capturing weekly seasonality in retail demand.
• Pitfall: Excessive lags introduce multicollinearity and overfit the model to noise.

Derived features that summarize the statistical properties of a moving time window. These capture local trends and volatility that raw lags miss.

• Common Functions: mean, std, min, max, quantile.
• Example: A 28-day rolling mean smooths out daily noise to reveal the underlying monthly trend.
• Tuning: The window size must align with the business cycle; a 7-day window captures weekly patterns, while a 90-day window captures quarterly shifts.

The process of extracting categorical and cyclical features from a timestamp index to expose recurring patterns. Models cannot natively interpret a datetime object.

• Categorical: day_of_week, month, quarter, is_holiday.
• Cyclical Encoding: Transforming hour or month into sin and cos components to preserve the circular nature (e.g., 23:00 is close to 00:00).
• Business Logic: Flags like is_payday or is_promotional_period are high-signal manual decompositions.

A smoothing technique that applies decaying weights to past observations, giving more importance to recent data. Unlike a simple rolling mean, EWMA reacts faster to sudden shifts.

• Parameter: The span or alpha controls the decay rate.
• Advantage: Reduces the lag bias inherent in simple moving averages.
• Application: Generating a responsive baseline for demand sensing when a sudden market shock occurs.

A method for encoding categorical variables by replacing them with a statistical summary of the target variable, calculated on a holdout or expanding window to prevent data leakage.

• Example: Encoding store_id with the average historical sales for that store.
• Time-Series Constraint: Must use expanding window or leave-one-out encoding to avoid using future information.
• Risk: Prone to overfitting on high-cardinality categories without proper smoothing.

A set of sine and cosine pairs used to model complex, multi-period seasonality as a deterministic function. This is a powerful alternative to dummy variables for capturing smooth cyclical patterns.

• Mechanism: A Fourier series decomposes a periodic signal into a sum of simple waves.
• Hyperparameter: The number of Fourier pairs (K) controls the smoothness of the fit.
• Use Case: Modeling dual seasonality (e.g., weekly and yearly) in a single linear model without requiring hundreds of lag features.