scholarly journals A Note on Mixed Stable Limit Theory for the OLSE and the Robustness of Subsampling Wald Tests

2015 ◽  
Author(s):  
Stelios Arvanitis
Keyword(s):  
Stable Limit ◽  
Limit Theory ◽  
Wald Tests

scholarly journals VECTOR AUTOREGRESSIONS WITH UNKNOWN MIXTURES OF I(0), I(1), AND I(2) COMPONENTS

2000 ◽  
Vol 16 (6) ◽  
pp. 905-926 ◽  
Author(s):  
Yoosoon Chang
Keyword(s):  
Limit Distribution ◽  
Nuisance Parameter ◽  
Estimation Method ◽  
Unit Roots ◽  
Wald Test ◽  
Vector Autoregressions ◽  
Chi Square ◽  
Limit Theory ◽  
Wald Tests ◽  
Linear Restrictions

This paper develops a new estimation method for nonstationary vector autoregressions (VAR's) with unknown mixtures of I(0), I(1), and I(2) components. The method does not require prior knowledge on the exact number and location of unit roots in the system. It is, therefore, applicable for VAR's with any mixture of I(0), I(1), and I(2) variables, which may be cointegrated in any form. The limit theory for the stationary component of our estimator is still normal, thereby preserving the usual VAR limit theory. Yet, the leading term of the nonstationary component of the estimator has mixed normal limit distribution and does not involve unit root distribution. Our method is an extension of the FM-VAR procedure by Phillips (1995, Econometrica 63, 1023–1078) and yields an estimator that is optimal in the sense of Phillips (1991, Econometrica 59, 283–306). Moreover, we show for a certain class of linear restrictions that the Wald tests based on the estimator are asymptotically distributed as a weighted sum of independent chi-square variates with weights between zero and one. For such restrictions, the limit distribution of the standard Wald test is nonstandard and nuisance parameter dependent. This has a direct application for Granger-causality testing in nonstationary VAR's.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

Sign in / Sign up

Export Citation Format

Share Document