A Constrained, Data-Driven Budgeting Framework Integrating Macro Demand Forecasting and Marketing Response Modeling

Yifei Lu; Hailin  Zhou; Yitian  Zhang

doi:10.51903/jtie.v4i3.466

Authors

Yifei Lu Computer Science, UCSD, University of California San Diego (UCSD), La Jolla, CA, USA
Hailin Zhou Applied Analytics, Columbia University, NY, USA
Yitian Zhang Accounting, The University of Wisconsin-Madison (UW-Madison), WI, USA

DOI:

https://doi.org/10.51903/jtie.v4i3.466

Keywords:

budget optimization, FP&A, demand forecasting, marketing mix

Abstract

Budgeting and financial planning & analysis (FP&A) increasingly require combining macroeconomic signals, channel-level marketing effectiveness, and hard accounting constraints into a single, auditable decision process. This paper proposes and empirically evaluates an end-to-end framework that (i) forecasts category-level demand from public macro data, (ii) learns diminishing-returns marketing response curves, and (iii) solves a constrained portfolio optimization problem to allocate marketing spend while satisfying SG&A and cash-flow guardrails consistent with real public-company statements. Using quarterly Personal Consumption Expenditures (PCE) components from FRED (durable goods, nondurable goods, and services) as a proxy for market demand, we compare seasonal naïve, SARIMAX, gradient boosting, and a multivariate VAR model in a rolling backtest (2018Q1-2025Q3). In parallel, we estimate marketing response from the Advertising dataset (TV, radio, and newspaper spend) via linear models, gradient boosting, and a Hill-function saturation model. We then calibrate financial constraints-gross margin, SG&A ratio, and operating cash-flow coverage-directly from Apple Inc.’s FY2025 Form 10-K filed with the SEC, and integrate all components into a Monte Carlo-evaluated budgeting optimizer. Results show that multivariate models improve total-demand accuracy (≈2.85% MAPE) and that nonlinear response curves indicate strong diminishing returns and negligible incremental value for newspaper spend. The constrained optimizer produces stable allocations that trade off expected operating profit and downside risk, and it highlights a practical insight: budgets that exactly meet a ratio-based cap under point forecasts may violate constraints under realistic demand uncertainty. The proposed workflow is fully reproducible from public data sources and provides a template for transparent, constraint-aware budgeting.

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