A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new path following algorithm for quadratic programming based on exact penalization. Similar penalties arise in $l_1$ regularization in model selection. Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the lasso and generalized lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well chosen examples illustrate the mechanics and potential of path following.Comment: 26 pages, 5 figure

On the Adaptive Partition Approach to the Detection of Multiple Change-Points

With an adaptive partition procedure, we can partition a “time course” into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age

Time-Scale Analysis of Sovereign Bonds Market Co-Movement in the EU

We study co-movement of 10-year sovereign bond yields of 11 EU countries. Our analysis is focused mainly on changes of co-movement in the crisis period, especially near two significant dates - the fall of Lehman Brothers, September 15, 2008, and the announcement of increase of Greek's public deficit in October 20, 2009. We study co-movement dynamics using wavelet analysis, it allows us to observe how co-movement changes across scales, which can be interpreted as investment horizons, and through time. We divide the countries into three groups; the Core of the Eurozone, the Periphery of the Eurozone and the states outside the Eurozone. Results indicate that co-movement considerably decreased in the crisis period for all countries pairs, however there are significant differences among the groups. Furthermore, we demonstrate that co-movement of bond yields significantly varies across scales

Business Cycle Asymmetry and the Stock Market

This paper investigates whether the systematic asymmetric behaviour of the US unemployment rate can be explained by the stock market. We consider threshold models to capture the asymmetric relationship between quarterly US unemployment rate and Dow Jones Industrial Average (DJ) stock returns. We test a range of null hypotheses of equlity restrictions against inequality constraints and the composite null hypothesis involving "steepness" in business cycles.UNEMPLOYMENT ; BUSINESS CYCLES ; MODELS