Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, in practice, identifiability issues have led many authors to abandon VARMA modeling in favor of the simpler Vector AutoRegressive (VAR) model. Such a practice is unfortunate since even very simple VARMA models can have quite complicated VAR representations. We narrow this gap with a new optimization-based approach to VARMA identification that is built upon the principle of parsimony. Among all equivalent data-generating models, we seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity, and that same penalty is then used to define an estimator that can be efficiently computed. We show that our estimator converges to a parsimonious element in the set of all equivalent data-generating models, in a double asymptotic regime where the number of component time series is allowed to grow with sample size. Further, we derive non-asymptotic upper bounds on the estimation error of our method relative to our specially identified target. Novel theoretical machinery includes non-asymptotic analysis of infinite-order VAR, elastic net estimation under a singular covariance structure of regressors, and new concentration inequalities for quadratic forms of random variables from Gaussian time series. We illustrate the competitive performance of our methods in simulation and several application domains, including macro-economic forecasting, demand forecasting, and volatility forecasting

Interpretable Vector AutoRegressions with Exogenous Time Series

The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that incorporate the impact of unmodeled exogenous variables (X) into the VAR. However, since the parameter space grows quadratically with the number of time series, estimation quickly becomes challenging. While several proposals have been made to sparsely estimate large VAR models, the estimation of large VARX models is under-explored. Moreover, typically these sparse proposals involve a lasso-type penalty and do not incorporate lag selection into the estimation procedure. As a consequence, the resulting models may be difficult to interpret. In this paper, we propose a lag-based hierarchically sparse estimator, called "HVARX", for large VARX models. We illustrate the usefulness of HVARX on a cross-category management marketing application. Our results show how it provides a highly interpretable model, and improves out-of-sample forecast accuracy compared to a lasso-type approach.Comment: Presented at NIPS 2017 Symposium on Interpretable Machine Learnin

High Dimensional Forecasting via Interpretable Vector Autoregression

Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by incorporating regularized approaches, such as the lasso in VAR estimation. Traditional approaches address overparameterization by selecting a low lag order, based on the assumption of short range dependence, assuming that a universal lag order applies to all components. Such an approach constrains the relationship between the components and impedes forecast performance. The lasso-based approaches work much better in high-dimensional situations but do not incorporate the notion of lag order selection. We propose a new class of hierarchical lag structures (HLag) that embed the notion of lag selection into a convex regularizer. The key modeling tool is a group lasso with nested groups which guarantees that the sparsity pattern of lag coefficients honors the VAR's ordered structure. The HLag framework offers three structures, which allow for varying levels of flexibility. A simulation study demonstrates improved performance in forecasting and lag order selection over previous approaches, and a macroeconomic application further highlights forecasting improvements as well as HLag's convenient, interpretable output

On subgroups in division rings of type 22

Let $D$ be a division ring with center $F$. We say that $D$ is a {\em division ring of type $2$} if for every two elements $x, y\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure

Collective leadership dynamics among professional peers: Co-constructing an unstable equilibrium

Professional service firms (PSFs) are characterised by contingent and contested power relations among an extended group of professional peers. Studies of such firms can therefore yield important insights for the literatures on collective leadership and leader–follower relations. Yet to date PSF scholars have neglected the topic of leadership,and leadership scholars have neglected the context of PSFs.Based on 102 interviewsacross the consulting, accounting, and legal sectors, we identify three relational processesthrough which professional peers co-construct collective leadership:legitimising, negotiating, and manoeuvring. We demonstrate how the relational processes taken together constitute an unstable equilibrium, both in the moment and over time, emphasising how leadership in PSFs is inherently contested and fragile. Our model contributes to theories of collective leadership and leader–follower relations by foregrounding the power and politics thatunderlie collective leadership. We highlight the significance of the individual leader within the collective. We challengeassumptionsconcerning the binary nature of leadership and followership,by showing how colleagues may grant leadership identities to their peers without necessarily granting them leadership authority, and without claiming follower identities for themselves

To what extent can headteachers be held to account in the practice of social justice leadership?

Internationally, leadership for social justice is gaining prominence as a global travelling theme. This article draws from the Scottish contribution to the International School Leadership Development Network (ISLDN) social justice strand and presents a case study of a relatively small education system similar in size to that of New Zealand, to explore one system's policy expectations and the practice realities of headteachers (principals) seeking to address issues around social justice. Scottish policy rhetoric places responsibility with headteachers to ensure socially just practices within their schools. However, those headteachers are working in schools located within unjust local, national and international contexts. The article explores briefly the emerging theoretical analyses of social justice and leadership. It then identifies the policy expectations, including those within the revised professional standards for headteachers in Scotland. The main focus is on the headteachers' perspectives of factors that help and hinder their practice of leadership for social justice. Macro systems-level data is used to contextualize equity and outcomes issues that headteachers are working to address. In the analysis of the dislocation between policy and reality, the article asks, 'to what extent can headteachers be held to account in the practice of social justice leadership?

Implementation of the Damages Directive in England & Wales

The Dossier discusses the questions arising from the need to implement the EU Damages Directive 2014/104/EU in several European Member States. My contribution focuses on the need for implementation in England & Wales

Soluble Cytokine Receptors (sIL-2Rα, sIL-2Rβ) Induce Subunit-Specific Behavioral Responses and Accumulate in the Cerebral Cortex and Basal Forebrain

Soluble cytokine receptors are normal constituents of body fluids that regulate peripheral cytokine and lymphoid activity. Levels of soluble IL-2 receptors (sIL-2R) are elevated in psychiatric disorders linked with autoimmune processes, including ones in which repetitive stereotypic behaviors and motor disturbances are present. However, there is no evidence that sIL-2Rs (or any peripheral soluble receptor) induce such behavioral changes, or that they localize in relevant brain regions. Here, we determined in male Balb/c mice the effects of single peripheral injections of sIL-2Rα or sIL-2Rβ (0–2 µg/male Balb/c mouse; s.c.) on novelty-induced ambulatory activity and stereotypic motor behaviors. We discovered that sIL-2Rα increased the incidence of in-place stereotypic motor behaviors, including head up head bobbing, rearing/sniffing, turning, and grooming behavior. A wider spectrum of behavioral changes was evident in sIL-2Rβ-treated mice, including increases in vertical and horizontal ambulatory activity and stereotypic motor movements. To our knowledge, this is the first demonstration that soluble receptors induce such behavioral disturbances. In contrast, soluble IL-1 Type-1 receptors (0–4 µg, s.c.) didn't appreciably affect these behaviors. We further demonstrated that sIL-2Rα and sIL-2Rβ induced marked increases in c-Fos in caudate-putamen, nucleus accumbens and prefrontal cortex. Anatomical specificity was supported by the presence of increased activity in lateral caudate in sIL-2Rα treated mice, while sIL-2Rβ treated mice induced greater c-Fos activity in prepyriform cortex. Moreover, injected sIL-2Rs were widely distributed in regions that showed increased c-Fos expression. Thus, sIL-2Rα and sIL-2Rβ induce marked subunit- and soluble cytokine receptor-specific behavioral disturbances, which included increases in the expression of ambulatory activity and stereotypic motor behaviors, while inducing increased neuronal activity localized to cortex and striatum. These findings suggest that sIL-2Rs act as novel immune-to- brain messengers and raise the possibility that they contribute to the disease process in psychiatric disorders in which marked increases in these receptors have been reported

Investigation of Low-Pressure Bimetallic Cobalt-Iron Catalyst-Grown Multiwalled Carbon Nanotubes and Their Electrical Properties

A bimetallic cobalt-iron catalyst was utilized to demonstrate the growth of multiwalled carbon nanotubes (CNTs) at low gas pressure through thermal chemical vapor deposition. The characteristics of multiwalled CNTs were investigated based on the effects of catalyst thickness and gas pressure variation. The results revealed that the average diameter of nanotubes increased with increasing catalyst thickness, which can be correlated to the increase in particle size. The growth rate of the nanotubes also increased significantly by ~2.5 times with further increment of gas pressure from 0.5 Torr to 1.0 Torr. Rapid growth rate of nanotubes was observed at a catalyst thickness of 6 nm, but it decreased with the increase in catalyst thickness. The higher composition of 50% cobalt in the cobalt-iron catalyst showed improvement in the growth rate of nanotubes and the quality of nanotube structures compared with that of 20% cobalt. For the electrical properties, the measured sheet resistance decreased with the increase in the height of nanotubes because of higher growth rate. This behavior is likely due to the larger contact area of nanotubes, which improved electron hopping from one localized tube to another