Hybrid Statistical–Fuzzy Decision Framework for Housing and Rental Price Dynamics: Evidence from Spain

Abstract

Real estate markets demand a nuanced comprehension of the evolving interplay between housing prices and rental rates. Traditional economic theory posits that rents drive property prices; however, contemporary evidence indicates a reversal, suggesting that fluctuations in housing prices can, in fact, influence rent levels. This study introduces a decision-support analytics framework to address this phenomenon, combining fractional integration (ARFIMA), fractional cointegration (FCVAR), and time–frequency domain causality analysis. Examination of the Spanish housing market yields three key insights. First, housing prices display persistent responses to shocks, causing rental rates to revert to equilibrium only over intermediate periods. Second, causality analyses reveal that property values significantly influence rental dynamics, confirming a directional effect. Third, long-term cointegration is evident, implying that rental adjustments facilitate the realignment of the housing–rental system towards equilibrium. The proposed framework equips real estate investors, policymakers, and urban planners with enhanced tools for decision-making, supporting refined risk assessment, optimal investment timing, and evidence-based housing affordability strategies. Overall, the findings advance management and economic policy-making by demonstrating how sophisticated time-series methodologies can inform sustainable housing market interventions.