arXiv 4 Jan 2020 · Statistics — Applications · publishedInternational Journal of Forecasting (2020) · 25 citations (OpenAlex)
arXiv:2001.01116 · PDF · DOI · OpenAlex · Extracted main text
We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gerlach, R. H., Chen, C. W., & Chan, N. Y. C (2011) Bayesian time-varying quantile forecasting for value-at-risk in financial markets | 0.928 | 4 | 3 | 100% |
| 2 | Koenker, R., & Xiao, Z (2006) Quantile autoregression | 0.644 | 2 | 2 | 100% |
| 3 | Nakajima, J., & West, M (2013) Bayesian analysis of latent threshold dynamic models | 0.511 | 2 | 1 | 100% |
| 4 | Neath, A. A., & Cavanaugh, J. E (2012) The bayesian information criterion: background, derivation, and applications | 0.405 | 1 | 1 | 100% |
| 5 | Youngman, B. D (2018) Generalized additive models for exceedances of high thresholds with an application to return level estimation for us wind gusts | 0.405 | 1 | 1 | 100% |
| 6 | Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I (1990) Stl: A seasonal-trend decomposition | 0.405 | 1 | 1 | 100% |
| 7 | Croux, C., Gelper, S., & Fried, R (2008) Computational aspects of robust holt-winters smoothing based on m-estimation | 0.405 | 1 | 1 | 100% |
| 8 | Choi, H. M., & Hobert, J. P (2013) Analysis of mcmc algorithms for bayesian linear regression with laplace errors | 0.405 | 1 | 1 | 100% |
| 9 | Chen, C., & Liu, L.-M (1993) Forecasting time series with outliers | 0.405 | 1 | 1 | 100% |
| 10 | Chen, C., & Liu, L.-M (1993) Joint estimation of model parameters and outlier effects in time series | 0.405 | 1 | 1 | 100% |
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