论文标题
贝叶斯的中位数自动赛稳定时间序列预测
Bayesian Median Autoregression for Robust Time Series Forecasting
论文作者
论文摘要
我们为时间序列预测开发了贝叶斯中位自回归（贝叶斯）模型。所提出的方法利用了中位数的时变分位回归，与广泛使用的基于均值的方法相比，中位回归的鲁棒性均可遗传。贝叶斯玛是由贝叶斯分数回归中的工作拉普拉斯似然方法进行的，通过将高斯误差更改为拉普拉斯，从而采用了与自回归模型相同的结构的参数模型，从而导致了时间序列预测的简单，健壮且可解释的模型。我们通过马尔可夫链蒙特卡洛估算模型参数。除了贝叶斯模型选择方法外，贝叶斯模型平均用于说明模型不确定性，包括自回归顺序的不确定性。使用模拟和实际数据应用程序说明了所提出的方法。与美国宏观经济数据预测的应用显示，与所选的基于均值的替代方案相比，贝叶斯玛会导致有利且通常是优越的预测性能，包括涵盖点和概率预测的各种损失函数。所提出的方法是通用的，可用于补充以自回归模型为基础的丰富方法。
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.
