Time Series Forecasting Cheat Sheet

Updated 2026-05-25

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Time series forecasting is the task of predicting future values based on historical sequential data ordered by time—fundamental to fields from finance and demand planning to weather prediction and infrastructure monitoring. Unlike cross-sectional analysis, forecasting must respect temporal dependencies, trends, and seasonality, making it uniquely challenging yet powerful. The landscape has evolved from classical statistical models like ARIMA and exponential smoothing through deep learning architectures and ensemble methods to foundation models pretrained on billions of observations that deliver zero-shot forecasting across diverse series—each tier suited to different data volumes, patterns, and horizons. A key insight: stationarity matters—most traditional models assume constant statistical properties over time, and transformations like differencing or decomposition often unlock otherwise intractable patterns.

What This Cheat Sheet Covers

This topic spans 17 focused tables and 106 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.

Table 1: Classical Statistical ModelsTable 2: Seasonal Decomposition TechniquesTable 3: Stationarity Testing and TransformationsTable 4: Autocorrelation AnalysisTable 5: Deep Learning RNN-Based ModelsTable 6: Transformer-Based ArchitecturesTable 7: Gradient Boosting and Tree-Based MethodsTable 8: MLP-Based and Convolutional Forecasting ModelsTable 9: Hybrid and Ensemble ApproachesTable 10: Foundation Models for Time SeriesTable 11: Feature Engineering for Time SeriesTable 12: Validation Strategies for Time SeriesTable 13: Forecast Evaluation MetricsTable 14: Handling Missing Data and OutliersTable 15: Probabilistic and Uncertainty QuantificationTable 16: Hierarchical and Global ForecastingTable 17: Advanced Topics and Emerging Methods

Table 1: Classical Statistical Models

ARIMA and exponential smoothing families remain the backbone of univariate forecasting—fast, interpretable, and tough to beat on small data. Understanding which model fits which pattern (trend, seasonality, volatility) determines whether you need a one-line call or a more complex pipeline.

Model	Example	Description
ARIMA	`ARIMA(2, 1, 1)`	• AutoRegressive Integrated Moving Average — combines past values (AR), differencing (I) for stationarity, and lagged errors (MA) • industry standard for univariate non-seasonal forecasting.
SARIMA	`SARIMA(1,1,1)(1,1,1,12)`	• Seasonal ARIMA — extends ARIMA with seasonal terms `(P,D,Q,m)` where `m` is the seasonal period • captures repeating patterns across cycles.
SARIMAX	`SARIMAX(1,1,1)(1,1,1,12)` `+ exog=[holidays, temp]`	SARIMA with eXogenous variables — incorporates external covariates (weather, promotions) that influence the target but are not predicted themselves.
Holt-Winters	`seasonal='additive'` `seasonal_periods=12`	• Triple exponential smoothing handling level, trend, and seasonality • additive for constant seasonal amplitude; multiplicative when seasonal variation scales with level.
Simple Exponential Smoothing	`alpha=0.3`	• Weighted average giving exponentially decreasing weight to older observations • suited for level-only series with no trend or seasonality • `alpha` controls smoothing strength
Holt's Linear Trend	`alpha=0.2, beta=0.1`	• Double exponential smoothing capturing level and linear trend • `alpha` smooths the level, `beta` smooths the trend component
ETS	`ETS(A, A, A)`	• ExponenTial Smoothing state space — formal framework with notation (Error, Trend, Seasonal) • 15 possible configurations • enables AIC-based model selection and generates valid prediction intervals

Table 1: Classical Statistical Models

Model	Example	Description
ARIMA	`ARIMA(2, 1, 1)`	• AutoRegressive Integrated Moving Average — combines past values (AR), differencing (I) for stationarity, and lagged errors (MA) • industry standard for univariate non-seasonal forecasting.
SARIMA	`SARIMA(1,1,1)(1,1,1,12)`	• Seasonal ARIMA — extends ARIMA with seasonal terms `(P,D,Q,m)` where `m` is the seasonal period • captures repeating patterns across cycles.
SARIMAX	`SARIMAX(1,1,1)(1,1,1,12)` `+ exog=[holidays, temp]`	SARIMA with eXogenous variables — incorporates external covariates (weather, promotions) that influence the target but are not predicted themselves.
Holt-Winters	`seasonal='additive'` `seasonal_periods=12`	• Triple exponential smoothing handling level, trend, and seasonality • additive for constant seasonal amplitude; multiplicative when seasonal variation scales with level.
Simple Exponential Smoothing	`alpha=0.3`	• Weighted average giving exponentially decreasing weight to older observations • suited for level-only series with no trend or seasonality • `alpha` controls smoothing strength
Holt's Linear Trend	`alpha=0.2, beta=0.1`	• Double exponential smoothing capturing level and linear trend • `alpha` smooths the level, `beta` smooths the trend component
ETS	`ETS(A, A, A)`	• ExponenTial Smoothing state space — formal framework with notation (Error, Trend, Seasonal) • 15 possible configurations • enables AIC-based model selection and generates valid prediction intervals