Key Forecasting Models

Why This Matters

Forecasting isn't just about predicting the future—it's about understanding why certain patterns emerge and how different variables interact over time. You're being tested on your ability to select the right model for specific data characteristics, whether that's handling seasonality, capturing nonlinear relationships, or working with limited historical data. The models in this guide represent fundamentally different approaches: some assume patterns repeat predictably, others model cause-and-effect relationships, and still others leverage machine learning to find hidden structures.

Don't just memorize model names and definitions. Know what type of data pattern each model handles best, when you'd choose one approach over another, and how models can be combined for better accuracy. Understanding the underlying mechanisms—stationarity requirements, weighting schemes, probabilistic frameworks—will help you tackle both multiple-choice questions and FRQ scenarios that ask you to justify model selection.

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Pattern-Based Time Series Models

These models assume that historical patterns—trends, cycles, and seasonal fluctuations—will continue into the future. The core mechanism is decomposing time-ordered data into predictable components.

Time Series Models

• Historical pattern analysis—examines data points collected at regular intervals to identify repeating structures like trends, seasonality, and cycles
• Stationarity assumption underlies many techniques; data properties like mean and variance should remain constant over time
• Foundation for specialized methods including ARIMA, exponential smoothing, and seasonal decomposition approaches

Moving Average Models

• Noise reduction through averaging—smooths short-term fluctuations by calculating means over a specified window of observations
• Simple vs. weighted approaches determine whether all points in the window contribute equally or recent data receives more emphasis
• Trend identification becomes clearer when random variation is filtered out, making underlying patterns visible

Exponential Smoothing Models

• Recency weighting—applies exponentially decreasing weights to older observations, making forecasts more responsive to recent changes
• Three complexity levels: simple (level only), double (level + trend), and triple/Holt-Winters (level + trend + seasonality)
• Short-term forecasting strength comes from quick adaptation to shifts in data patterns without requiring extensive parameter tuning

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Stationary and Seasonal Adjustments

These models explicitly handle non-stationary data and periodic fluctuations. The key mechanism is transforming data or adding components to capture time-dependent structures.

ARIMA Models

• Three-component structure—combines autoregressive (AR) terms, differencing (I), and moving average (MA) components in a unified framework
• Parameters $(p, d, q)$ must be identified: $p$ = AR order, $d$ = differencing degree, $q$ = MA order
• Stationarity through differencing—the "I" component transforms non-stationary data by computing differences between consecutive observations

Seasonal Models

• Periodic pattern capture—explicitly models fluctuations that repeat at fixed intervals (weekly, monthly, quarterly, annually)
• SARIMA extension adds seasonal parameters $(P, D, Q, s)$ to standard ARIMA for data with both trend and seasonality
• Industry applications are critical in retail, agriculture, tourism, and energy where demand follows predictable calendar patterns

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Relationship-Based Models

Rather than relying solely on historical patterns, these models examine how variables influence each other. The mechanism involves quantifying dependencies between predictors and outcomes.

Regression Models

• Variable relationships—establishes mathematical connections between a dependent variable (what you're predicting) and independent variables (predictors)
• Linear form $y = \beta_0 + \beta_1 x_1 + ... + \beta_n x_n + \epsilon$ assumes additive effects; nonlinear variants capture curved relationships
• Coefficient interpretation reveals the magnitude and direction of each predictor's impact on the forecast

Causal Models

• Cause-and-effect focus—goes beyond correlation to identify which variables actually drive outcomes rather than just move together
• Confounding control requires careful variable selection to isolate true causal relationships from spurious associations
• Intervention analysis in econometrics and policy evaluation—predicts what happens when you change a variable, not just observe it

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Advanced and Flexible Approaches

These models handle complexity that traditional methods can't capture—nonlinear patterns, limited data, or situations requiring human expertise. The mechanisms range from artificial intelligence to probabilistic updating to expert judgment.

Neural Network Models

• Nonlinear pattern recognition—artificial neurons in interconnected layers can model complex, non-obvious relationships in data
• Large data requirements for training; networks learn patterns from examples rather than from pre-specified equations
• Computational intensity and "black box" nature make interpretation challenging, but predictive power often exceeds traditional methods

Bayesian Forecasting Models

• Prior + evidence updating—starts with initial beliefs (priors) and systematically revises them as new data arrives using Bayes' theorem
• Uncertainty quantification produces probability distributions rather than point estimates, showing the range of likely outcomes
• Small-sample strength—particularly valuable when historical data is limited because prior knowledge supplements sparse observations

Judgmental Forecasting Methods

• Expert-driven predictions—relies on human knowledge, experience, and qualitative assessment rather than purely statistical analysis
• Data-scarce situations like new product launches, unprecedented events, or emerging markets where historical patterns don't exist
• Hybrid approaches combine expert judgment with quantitative models through techniques like Delphi method or scenario planning

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Quick Reference Table

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Self-Check Questions

1. Which two models both use weighted combinations of past observations but differ in how they assign those weights? What's the key distinction?

2. You're forecasting quarterly retail sales that show clear holiday spikes. Which model category would you choose, and what parameters would you need to specify?

3. Compare and contrast regression models and causal models. In what situation would a regression forecast be misleading while a causal model would be appropriate?

4. A startup wants to forecast demand for a product category that didn't exist two years ago. Why might Bayesian or judgmental methods outperform ARIMA in this scenario?

5. An FRQ describes a dataset with a clear upward trend, strong December peaks, and random daily noise. Outline which model you'd select and justify your choice by explaining what each component of the model addresses.