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Many real time series datasets exhibit structural changes over time. A popular model for capturing their temporal dependence is that of vector autoregressions (VAR), which can accommodate structural changes through time evolving transition matrices. The problem then becomes to both estimate the (unknown) number of structural break points, together with the VAR model parameters. An additional challenge emerges in the presence of very large datasets, namely on how to accomplish these two objectives in a computational efficient manner. In this article, we propose a novel procedure which leverages a block segmentation scheme (BSS) that reduces the number of model parameters to be estimated through a regularized least-square criterion. Specifically, BSS examines appropriately defined blocks of the available data, which when combined with a fused lasso-based estimation criterion, leads to significant computational gains without compromising on the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with new local and exhaustive search steps to consistently estimate the number and relative location of the break points. The procedure is scalable to big high-dimensional time series datasets with a computational complexity that can achieve O(n), where n is the length of the time series (sample size), compared to an exhaustive procedure that requires steps. Extensive numerical work on synthetic data supports the theoretical findings and illustrates the attractive properties of the procedure. Finally, an application to a neuroscience dataset exhibits its usefulness in applications. Supplementary files for this article are available online. 

Surface ocean temperature and velocity anomalies at meso‐ and sub‐meso‐scales induce wind stress anomalies. These wind‐front interactions, referred to as thermal (TFB) and current (CFB) feedbacks, respectively, have been studied in isolation at mesoscale, yet they have rarely been considered in tandem. Here, we assess the combined influence of TFB and CFB and their relative impact on surface wind stress derivatives. Analyses are based on output from two regions of the Southern Ocean in a coupled simulation with local ocean resolution of 2 km. Considering both TFB and CFB shows regimes of interference, which remain mostly linear down to the simulation resolution. The jointly‐generated wind stress curl anomalies approach 10⁻⁵ N m⁻³, ∼20 times stronger than at mesoscale. The synergy of both feedbacks improves the ability to reconstruct wind stress curl magnitude and structure from both surface vorticity and SST gradients by 12%–37% on average, compared with using either feedback alone.

 

Abstract Topographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts.