A Nonlinear Target-Factor Model with Attention Mechanism for Mixed-Frequency Data
Alessio Brini, Ekaterina Seregina
TL;DR
This work develops MPTE, a Transformer-based framework for estimating latent factors from mixed-frequency panel data with nonlinear signals. It unifies target and auxiliary information through cross-sectional and temporal attention, generalizing Target PCA and enabling transfer-learning gains without resampling. The authors establish consistency and asymptotic normality in the linear case, extend the model to nonlinear signal extraction via a Transformer encoder, and demonstrate superior performance in simulations and macroeconomic forecasting with interpretable attention patterns. The approach provides a flexible, data-driven method for leveraging heterogeneous information sources in high-dimensional time series, with practical relevance for policy analysis and forecasting due to its transparency and adaptability.
Abstract
We propose Mixed-Panels-Transformer Encoder (MPTE), a novel framework for estimating factor models in panel datasets with mixed frequencies and nonlinear signals. Traditional factor models rely on linear signal extraction and require homogeneous sampling frequencies, limiting their applicability to modern high-dimensional datasets where variables are observed at different temporal resolutions. Our approach leverages Transformer-style attention mechanisms to enable context-aware signal construction through flexible, data-dependent weighting schemes that replace fixed linear combinations with adaptive reweighting based on similarity and relevance. We extend classical principal component analysis (PCA) to accommodate general temporal and cross-sectional attention matrices, allowing the model to learn how to aggregate information across frequencies without manual alignment or pre-specified weights. For linear activation functions, we establish consistency and asymptotic normality of factor and loading estimators, showing that our framework nests Target PCA as a special case while providing efficiency gains through transfer learning across auxiliary datasets. The nonlinear extension uses a Transformer architecture to capture complex hierarchical interactions while preserving the theoretical foundations. In simulations, MPTE demonstrates superior performance in nonlinear environments, and in an empirical application to 13 macroeconomic forecasting targets using a selected set of 48 monthly and quarterly series from the FRED-MD and FRED-QD databases, our method achieves competitive performance against established benchmarks. We further analyze attention patterns and systematically ablate model components to assess variable importance and temporal dependence. The resulting patterns highlight which indicators and horizons are most influential for forecasting.