Forecasting Time-Varying Correlation Matrices with Large Language Models

Georgii Petrov, Ilya Novitskiy, Mironov Kirill Sergeevich, Sergey Muravyov, Valeria Efimova, Viacheslav Shalamov

Keywords: large language models, correlation matrix forecasting, LLM-as-a-Prophet, zero-shot prompting, chain-of-thought, structured JSON output, PSD calibration, time-varying correlation, financial time series, soft-persistence operator

TL;DR: Zero-shot LLMs forecast financial correlation matrices directly as JSON, closing ~5% of the persistence-to-oracle gap at h=22 on two daily panels, but behave as a soft-persistence operator that understates magnitude vs calibrated shrinkage.

Abstract: Forecasting a time-varying correlation matrix is a core financial prediction problem: portfolio variance, value-at-risk, and composite stress indices are all non-linear functions of it, and a valid forecast must stay on a constrained manifold - symmetric, unit-diagonal, positive semidefinite. We ask whether a pre-trained large language model (LLM) can do this zero-shot. We prompt Anthropic Claude to read a short history of a five-asset panel and emit the next correlation matrix directly as JSON; a light eigenvalue-repair step fixes the rare invalid output, and is needed on only ~2% of calls. On two daily panels (Russia financial-stress sub-indices and Eurostoxx country returns) chain-of-thought prompting beats the persistence baseline at multi-week horizons, by a margin that grows monotonically with the horizon and reaches about +5% of the persistence-to-oracle error gap at the one-month horizon on both panels; at the one-day horizon, where persistence is near-perfect, it does not. The LLM does not beat the strongest classical baseline, exponential smoothing toward the long-run average. We explain why, and show that the LLM is not merely a worse version of that baseline: it moves the matrix in a genuinely different and informative direction, but takes too small a step. This points to hybrid forecasters that keep the LLM's direction and borrow a classical method's magnitude.

Submission Number: 151