Payments Forecasting with Retail Data

Who am I?

• Bruce Hicks – Founder and Principal, est8ic.ai
• 15+ years of experience in ML, forecasting and economic analysis
• Working with Global FinTech companies
• Started my career in technology-enabled manufacturing

Framework for today's talk - forecasting

Organizations of any size need:

• To forecast revenue
• Using a precise approach
• Easily with little complexity
• Providing clear insight — "What changed and Why"
• Establishing and maintaining credibility with stakeholders

Agenda

1. The Challenge — statistical issues in operational data
2. The Structural Solution — modeling with macroeconomic indices
3. Building It Right — functional form, indexation, and regression rigor
4. Modeling Dynamics — stationarity, co-integration, and AR models
5. Using the Forecast — uncertainty, scenarios, and stakeholder communication
6. Maintaining the Model — tracking drift and maintaining accuracy

Statistical Issues

Top 2 key considerations when modeling:

Sampling Bias

• Empirical studies suffer from bias in observational and operational data
• Affects inference, parameter bias, and generalizability

Simultaneity Bias

• Joint determination of explanatory and dependent variables
• Examples from economics — demand pull inflation

So what do we do about it?

We need structure

• Naive models inherit these biases — they lack economic grounding
• A structural approach decomposes revenue into interpretable, testable components
• Map macro forces → industry dynamics → operational drivers → financial outcomes
• Each layer is independently observable, forecastable, auditable, and composable

Dynamic Systems

A Structural Simplified Linear Approach

• Overcoming differing cyclicality — separate the pro, counter, and a-cyclical components
• Functional form — linearizing PVM: pricing, volume, mix
• Implications and opportunities — stability and long-run forecasts
  • Things to monitor — market penetration, share, pricing mix, etc.

System Dynamics

Modeling Change — generating insight, preventing drift

• Natural log — log-log, log-level
• Indicator functions — technology transformations, share changes, pricing mix
  • Intercept/s
  • Slope/s
  • Trend

Indexation — Pricing and Volume Shifts

Connect public macro data to your revenue

• Weighting factors : regional, industry, product mix
  • Choice of metric matters — revenue-weighted vs. volume-weighted vs. transaction-weighted
• segmentation: firmographics, product categories
• Weights are calibrations — when mix shifts, re-weight or the forecast silently degrades

Model

Functional Form

• Revenue is multiplicative:
• Logs make it linear:
  • Every coefficient directly actionable — scenarios, monitoring, communication
  • Full OLS diagnostic toolkit
  • Returns to scale estimated, not assumed — the data tells you the regime
• Trend: time-varying intercept and elasticities — test with indicators
• Seasonality: periodic (calendar) and non-periodic (Easter, promotions) — both modeled explicitly

Model

Index approach

Model

Index approach

Industry Index

Pricing Mix

• Weighting factors:

Regression Modeling — key concepts

Identification — can feel like an art form, how to know it's right

• Specification — Functional Form drives everything downstream
  • Omitted Variable Bias — dropping a variable biases what remains
    (e.g., dropping a collinear predictor that carries unique signal)
  • Collinearity (VIF) — individual t-tests become unreliable;
    doesn't mean the model is wrong — check joint significance
  • Heteroscedasticity — tells you about the DGP, not just the errors
  • Autocorrelation — often the first signal of a missing variable

Go/No-Go

• F-Test — joint significance holds even when individual t-tests fail
• Out-of-sample validation — the only test that matters for forecasting

Regression Modeling — key concepts

Interpretation and Validation

• Ceteris paribus — isolate the effect of one driver, holding others constant
  • The structural decomposition makes this operational, not just theoretical
• Accuracy metrics — match the metric to the audience:
  • MAPE for stakeholders — "the forecast was off by 0.8%"
  • MAE for robustness — resistant to outlier distortion
  • RMSE for risk — penalizes for the misses that hurt most
• Out-of-sample accuracy is the credibility test — in-sample fit is necessary, not sufficient

Regression Modeling — Key Concepts

Leveraged Outliers — What's driving your model?

• Leverage: — voting power of each observation

  • near 0 → negligible influence; near 1 → model anchored to this point
  • Flag:

• Influence:

  • Large shift → this observation is driving your estimates

• Action: structural break → indicator (slide 10); data issue → investigate

• ; leveraged outlier when both and

Regression Modeling — key concepts

Other key concepts

• Causal inference — identifying causal relationships
  • Instrumental variables — addressing endogeneity e.g., 2SLS
  • Difference-in-differences — comparing treatment and control groups
  • Regression discontinuity design — exploiting discontinuities in treatment assignment

Advanced Time Series Modeling

Stationarity — The precondition

• I(0) vs. I(1) — does the series revert to a mean, or drift without bound?
  • Get this wrong → spurious regression: high , meaningless coefficients
  • Test before modeling — ADF, KPSS
• Modeling choice: levels (if stationary or co-integrated) vs. differences

Co-integration — Validating the structural link

• Integrated processes don't need differencing if the model captures a real equilibrium
  • Co-integration means the linear combination is stationary (residual)
• Error correction — deviations from equilibrium self-correct; the forecast adapts

Advanced Time Series Modeling

ARIMA Errors

• HAC standard errors — corrects inference for heteroscedasticity and autocorrelation in one step; doesn't change
• Autocorrelation in residuals is a symptom — often signals a missing variable (OVB)
  • Fix the specification first; add AR terms only as a last resort
• Parsimony — minimum lag order

Forecasting

Forecast Uncertainty

• Minimize model error — diagnostic rigor delivers <1% cumulative MAPE on 12-month holdout
• Forecast error = model error + input forecast error
  — negligible model error materially improves structural decomposition
• β × ΔX decomposition — attribute the forecast to each component: what moved, by how much, and why
• Macro shocks → revenue impact — calibrate a GDP or index miss directly to your bottom line
• Scenarios — "what if" analysis is where strategy meets forecasting

Forecasting

Key forecast comparison techniques

• Key Risks and Scenario planning — how you talk to the street
• Current vs. prior — year, forecast, scenario
• Decision-oriented evaluation — financial mitigation analysis

Monitoring and Evaluation

Evaluation — What the framework enables

• Performance tracking — within-year vs. full-year error, error correction, trending to plan
• Early warning — residual structure and parameter stability signal problems before the forecast misses
• Overlay adjustments — model is the baseline, layer business assumptions on top e.g., large deals, business shifts
• Model updating — drift has meaning, meaning has value; update when diagnostics dictate

Monitoring and Evaluation

Monitoring

What to version and track:
Given a functional form:
Where

• , , , , , — as a versioned table
• coefficient vector
• — generally correct, and any other transformations
• Holdout by estimation vintage

Monitoring and Evaluation

Assumptions That Cause Drift

• Share changes — if your revenue mix shifts, the index weights go stale
• Pricing mix — changes in what's sold at what price point
• Product mix — new products, retired products, category shifts
• Industry composition — your segments grow at different rates
• Regional mix — geographic exposure changes

Key Takeaways

• Structure over complexity — decompose revenue through macro → industry → operational → financial layers for interpretable, drift-resistant forecasts
• Regression rigor matters — proper identification, diagnostics, and out-of-sample validation separate credible forecasts from fragile ones
• Monitor the assumptions — share changes, pricing mix, and industry composition drift will break even well-specified models if untracked
• Communicate uncertainty — scenarios and comparison frameworks build stakeholder credibility over point forecasts

Questions?

Thank you

Bruce Hicks
Founder and Principal, est8ic.ai