We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are scanned for multiple change points using a moving window-based procedure, which is followed by a location refinement stage. MOSEG enjoys computational efficiency thanks to the adoption of a coarse grid in the first stage, and achieves theoretical consistency in estimating both the total number and the locations of the change points, under general conditions permitting serial dependence and non-Gaussianity. We also propose MOSEG.MS, a multiscale extension of MOSEG which, while comparable to MOSEG in terms of computational complexity, achieves theoretical consistency for a broader parameter space where large parameter shifts over short intervals and small changes over long stretches of stationarity are simultaneously allowed. We demonstrate good performance of the proposed methods in comparative simulation studies and in an application to predicting the equity premium.

翻译：我们针对高维线性回归问题提出一种数据分割方法，其中回归参数允许发生多次变化。该方法名为MOSEG，包含两个阶段：首先，采用基于滑动窗口的程序扫描数据以检测多个变点；随后进入位置精修阶段。由于第一阶段采用粗粒度网格，MOSEG具有计算高效性，并且在允许序列依赖和非高斯性的通用条件下，能够实现变点总数和位置估计的理论一致性。我们还提出MOSEG的多尺度扩展版本MOSEG.MS，其在计算复杂度与MOSEG相当的同时，能在更广泛的参数空间内实现理论一致性——该空间可同时包含短时间间隔内的大幅参数偏移和长时间平稳段内的微小变化。通过对比模拟实验和预测权益溢价的实证应用，我们验证了所提方法的优异性能。