Boosting for Time Series and an Application to Value at Risk Forecasting

Abstract:

We introduce BlockBoost1, a boosting algorithm for time series forecasting with provable generalization guarantees. Standard boosting algorithms inherit the i.i.d. assumption of the PAC learning framework, which temporal dependence violates by design. BlockBoost addresses this at the algorithmic level by replacing instance-wise weight updates with block-wise updates over contiguous temporal segments, constraining the weight sequence to a block-constant subspace of the probability simplex. We prove that this modification drives the block-wise empirical risk to zero, introduces implicit regularization against noise memorization, and yields a generalization bound for stationary β-mixing sequences. We further prove that locally stationary processes – a class encompassing most financial return series – can be approximated in L2 by a strictly stationary β-mixing process under mild regularity conditions, extending the learning guarantees to this broader setting. A regression variant, BlockBoost.R2, is derived and applied to Value at Risk forecasting on four equity indices across three markets: the WAEMU regional exchange, the CAC 40, and the S&P 500. Evaluated over 2014–2026 via standard backtesting procedures, BlockBoost achieves superior unconditional coverage at the 5% confidence level across all markets, with the advantage most pronounced in frontier markets where parametric distributional assumptions are misspecified. At the 1% level, GARCH models with heavy-tailed innovations retain an edge, attributable to their capacity to extrapolate into the extreme tail from limited data. These results establish BlockBoost as a theoretically grounded and empirically competitive alternative to the GARCH family for financial risk measurement.

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