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Bayesian MIDAS Penalized Regressions Estimation Selection and Prediction

  • KanKan
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Document pages: 48 pages

Abstract: We propose a new approach to mixed-frequency regressions in ahigh-dimensional environment that resorts to Group Lasso penalization andBayesian techniques for estimation and inference. In particular, to improve theprediction properties of the model and its sparse recovery ability, we considera Group Lasso with a spike-and-slab prior. Penalty hyper-parameters governingthe model shrinkage are automatically tuned via an adaptive MCMC algorithm. Weestablish good frequentist asymptotic properties of the posterior of thein-sample and out-of-sample prediction error, we recover the optimal posteriorcontraction rate, and we show optimality of the posterior predictive density.Simulations show that the proposed models have good selection and forecastingperformance in small samples, even when the design matrix presentscross-correlation. When applied to forecasting U.S. GDP, our penalizedregressions can outperform many strong competitors. Results suggest thatfinancial variables may have some, although very limited, short-term predictivecontent.

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