Learning the Coefficients of the Standard Volatility Forecaster

Volatility is the scale of asset-price fluctuations, and forecasting it is central to financial risk management. The heterogeneous autoregressive (HAR) model is a widely used, interpretable linear model that forecasts future volatility from its daily, weekly, and monthly averages, but holds the weights on those averages fixed over time. This paper makes two contributions. First, we introduce Time-Varying HAR (TV-HAR), in which a small neural network uses current market conditions to generate the HAR coefficients for each day, preserving the model's interpretable form while allowing its effective memory to adapt. Second, we present an evolutionary, LLM-driven framework in which a language model proposes forecasting formulations from a constrained set of volatility-model components and a fixed evaluator guides the search. In walk-forward experiments on 51 evaluation series drawn from a panel of 19 equity indices and 40 US stocks, TV-HAR outperforms fixed- and smooth-transition HAR at one-, five-, and 22-day horizons, reducing median QLIKE relative to expanding-window HAR by approximately 7\%, 15\%, and 4\%, while the strongest of the 214 formulations proposed by the LLM-driven evolutionary search build on TV-HAR and yield modest additional gains at short horizons.