A Nonlinear Target-Factor Model with Attention Mechanism for Mixed-Frequency Data

Abstract

We propose the Mixed-Panels-Transformer Encoder (MPTE), a framework for estimating factor models in panels with mixed frequencies and nonlinear signals. Classical factor models rely on linear signal extraction and homogeneous sampling frequencies, limiting their use when variables arrive at different frequencies. MPTE instead uses Transformer-style attention to construct context-aware signals, replacing fixed linear combinations with adaptive reweighting. We extend principal component analysis to accommodate general temporal and cross-sectional attention operators, so the model learns to aggregate information across frequencies without manual alignment. Under linear activations, we establish consistency and asymptotic normality of factor and loading estimators, show that the framework nests classical factor models as a special case, and obtain efficiency gains through transfer learning across auxiliary panels. A Transformer architecture handles the nonlinear case, which we assess through simulations and an empirical application. In simulations, MPTE outperforms linear benchmarks under nonlinear designs. On 13 quarterly U.S. macroeconomic targets drawn from 48 monthly and quarterly FRED series, it remains competitive with established benchmarks. By averaging learned attention across variables and time, we recover target-specific variable importance and lag relevance, and ablations quantify the contribution of each model component.