Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow a stationary autoregressive integrated moving average (ARIMA) model, or its seasonal variants, which are unable to capture a long-range dependence structure (long memory) of the error process. We propose a novel dynamic linear regression model that incorporates the long-range dependence feature of the errors and show that the proposed error process may: (i) have a significant impact on the posterior uncertainty of the estimated regression parameters and (ii) improve the model's forecasting ability. We develop a Markov chain Monte Carlo method to fit general dynamic linear regression models based on a frequency domain approach that enables fast, asymptotically exact Bayesian inference for large datasets. We demonstrate that our approximate algorithm is faster than the traditional time domain approaches, such as the Kalman filter and the multivariate Gaussian likelihood, while producing a highly accurate approximation to the posterior. The method is illustrated in simulated examples and two energy forecasting applications, showing that it outperforms approaches that do not account for semi-long memory, as well as a state-of-the-art neural-network-based forecasting procedure.

翻译：动态线性回归模型通过一组外生时间序列的线性组合来预测时间序列的值，同时结合误差项的时间序列过程。该误差过程通常假设服从平稳的自回归积分滑动平均（ARIMA）模型或其季节性变体，但这些模型无法捕捉误差过程的长期依赖结构（长记忆性）。我们提出一种新颖的动态线性回归模型，该模型融合了误差的长程依赖特征，并表明所提出的误差过程可能：（i）显著影响估计回归参数的后验不确定性，（ii）提升模型的预测能力。我们开发了一种基于频域方法的马尔可夫链蒙特卡罗算法，用于拟合一般动态线性回归模型，该方法能够对大规模数据集实现快速、渐近精确的贝叶斯推断。实验证明，我们的近似算法比传统的时域方法（如卡尔曼滤波器和多元高斯似然）更快，同时产生高度精确的后验近似。该方法在模拟示例和两个能源预测应用中得到了验证，结果表明其优于未考虑半长记忆性的方法以及基于神经网络的最新预测程序。