On the quasi-derivation relation for multiple zeta values

Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relation for multiple zeta values. The goal of the present paper is to present a proof of this conjecture by reducing it to a class of relations for multiple zeta values studied by Kawashima. In addition, some algebraic aspects of the quasi-derivation operator $\partial_n^{(c)}$ on $\mathbb{Q}< x,y>$, which was defined by modeling a Hopf algebra developed by Connes and Moscovici, will be presented.Comment: 14 page

Rooted tree maps and the derivation relation for multiple zeta values

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between multiple zeta values. In this note we show that the derivation relations for multiple zeta values are contained in this class of linear relations.Comment: 6 page

Testing for common breaks in a multiple equations system

The issue addressed in this paper is that of testing for common breaks across or within equations. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that some subsets of the parameters (either regression coe cients or elements of the covariance matrix of the errors) share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test con- sidered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Also of indepen- dent interest, we provide results about the consistency and rate of convergence when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as the number of parameters in the model. Sim- ulation results show that the test has good nite sample properties. We also provide an application to various measures of in ation to illustrate its usefulness

Testing for common breaks in a multiple equations system

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations. Under the alternative hypothesis, the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Of independent interest, we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size, allowing break dates not separated by a positive fraction of the sample size across equations. Simulations show that the test has good finite sample properties. We also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness.Accepted manuscrip

Testing for Common Breaks in a Multiple Equations System

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations. Under the alternative hypothesis, the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Of independent interest, we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size, allowing break dates not separated by a positive fraction of the sample size across equations. Simulations show that the test has good finite sample properties. We also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness.Comment: 44 pages, 2 tables and 1 figur

Testing for common breaks in a multiple equations system

The issue addressed in this paper is that of testing for common breaks across or within equations. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that some subsets of the parameters (either regression coe cients or elements of the covariance matrix of the errors) share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Also of independent interest, we provide results about the consistency and rate of convergence when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as the number of parameters in the model. Simulation results show that the test has good nite sample properties. We also provide an application to various measures of in ation to illustrate its usefulness