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Random subspace methods are a novel approach to obtain accurate forecasts in high-dimensional regression settings. Forecasts are constructed from random subsets of predictors or randomly weighted predictors. We provide a theoretical justification for these strategies by deriving bounds on their asymptotic mean squared forecast error, which are highly informative on the scenarios where the methods work well. Monte Carlo simulations confirm the theoretical findings and show improvements in predictive accuracy relative to widely used benchmarks. The predictive accuracy on monthly macroeconomic FRED-MD data increases substantially, with random subspace methods outperforming all competing methods for at least 66% of the series.
We derive optimal weights for Markov switching models by weighting observations such that forecasts are optimal in the MSFE sense. We provide analytic expressions of the weights conditional on the Markov states and conditional on state probabilities. This allows us to study the effect of uncertainty around states on forecasts. It emerges that, even in large samples, forecasting performance increases substantially when the construction of optimal weights takes uncertainty around states into account. Performance of the optimal weights is shown through simulations and an application to US GNP, where using optimal weights leads to significant reductions in MSFE.
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