Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data is continually arriving and is analyzed adaptively. We are concerned with the related, but distinct, offline version, in which retrospective analysis of an entire sequence is performed. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the αth absolute moment, for some α ∈ (0, 2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs. We conclude with applications in genetics, finance and spatio-temporal analysis.

Many prokaryotic protein complexes underlie polar asymmetry. In Caulobacter crescentus, a flagellum is built exclusively at the pole that arose from the previous cell division. The basis for this pole specificity is unclear but could involve a cytokinetic birth scar that marks the newborn pole as the flagellum assembly site. We identified two developmental proteins, TipN and TipF, which localize to the division septum and the newborn pole after division. We show that septal localization of TipN/F depends on cytokinesis. Moreover, TipF, a c-di-GMP phosphodiesterase homolog, is a flagellum assembly factor that relies on TipN for proper positioning. In the absence of TipN, flagella are assembled at ectopic locations, and TipF is mislocalized to such sites. Thus TipN and TipF establish a link between bacterial cytokinesis and polar asymmetry, demonstrating that division does indeed leave a positional mark in its wake to direct the biogenesis of a polar organelle.

There are many different ways in which change point analysis can be performed, from purely parametric methods to those that are distribution free. The ecp package is designed to perform multiple change point analysis while making as few assumptions as possible. While many other change point methods are applicable only for univariate data, this R package is suitable for both univariate and multivariate observations. Hierarchical estimation can be based upon either a divisive or agglomerative algorithm. Divisive estimation sequentially identifies change points via a bisection algorithm. The agglomerative algorithm estimates change point locations by determining an optimal segmentation. Both approaches are able to detect any type of distributional change within the data. This provides an advantage over many existing change point algorithms which are only able to detect changes within the marginal distributions.

The vector autoregression (VAR) has long proven to be an effective method for modeling the joint dynamics of macroeconomic time series as well as forecasting. A major shortcoming of the VAR that has hindered its applicability is its heavy parameterization: the parameter space grows quadratically with the number of series included, quickly exhausting the available degrees of freedom. Consequently, forecasting using VARs is intractable for low-frequency, high-dimensional macroeconomic data. However, empirical evidence suggests that VARs that incorporate more component series tend to result in more accurate forecasts. Conventional methods that allow for the estimation of large VARs either tend to require ad hoc subjective specifications or are computationally infeasible. Moreover, as global economies become more intricately intertwined, there has been substantial interest in incorporating the impact of stochastic, unmodeled exogenous variables. Vector autoregression with exogenous variables (VARX) extends the VAR to allow for the inclusion of unmodeled variables, but it similarly faces dimensionality challenges.We introduce the VARX-L framework, a structured family of VARX models, and provide methodology that allows for both efficient estimation and accurate forecasting in high-dimensional analysis. VARX-L adapts several prominent scalar regression regularization techniques to a vector time series context in order to greatly reduce the parameter space of VAR and VARX models. We also highlight a compelling extension that allows for shrinking toward reference models, such as a vector random walk. We demonstrate the efficacy of VARX-L in both lowand high-dimensional macroeconomic forecasting applications and simulated data examples. Our methodology is easily reproducible in a publicly available R package.

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