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Abstract:
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Variable selection is crucial in many econometric and financial modeling problems, especially for forecasting using high-dimensional predictors. Regularization methods are commonly used to reduce the dimensionality. Besides that, some heuristic algorithms are also appealing to find the best subset of variables. This paper compares four groups of variable selection algorithms through comprehensive simulation studies and application on macroeconomic forecasting: (1) traditional methods including forward selection and greedy exchange algorithm (2) L1 regularization including adaptive LASSO, (3) L0 regularization including iterative hard thresholding and hard thresholding pursuit (4) heuristic algorithms including simulated annealing and SMC. Different dimensionality setting (moderate high dimension and ultra-high dimension), sample size, signal strength and dependence setting among predictors (independent and dependent) are considered and their performance in terms of variable selection and out-of-sample prediction are investigated. Finally, these methods are applied to the FRED-MD database to evaluate their forecasting performance compared with diffusion index approach.
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