Long-Memory Business Cycles: A Fractionally Integrated Equilibrium Model with an Irreducible Forecast Floor

Standard business-cycle models are driven by shocks that fade within a few years. Real output does not behave that way. A shock lingers for decades, decaying slowly, a property called long memory. This paper builds an equilibrium model whose driver has genuine long memory and asks what the usual short-memory setups structurally cannot do. Long memory reshapes how shocks propagate, leaves the model with a single well-defined equilibrium, and puts the best possible forecast permanently out of reach for any fixed-size model. In United States output the memory is high, close to a unit root, and a long-memory forecaster beats standard benchmarks at longer horizons. The paper studies real output only, is careful about what can and cannot be identified, and reports where the short-memory benchmark still wins.