52,149 research outputs found
Nonlinear Cointegrating Regression under Weak Identification
An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.Integrated process, Local time, Nonlinear regression, Uniform weak convergence, Weak identification
Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500
Published in International Economic Review, https://doi.org/10.1111/iere.12132</p
Testing for Multiple Bubbles 2: Limit Theory of Real Time Detectors
Singapore MOE Academic Research Tier 2Published in International Economic Review, https://doi.org/10.1111/iere.12131</p
: An Excellent Candidate of Tetraquarks
We analyze various possible interpretations of the narrow state
which lies 100 MeV above threshold. This interesting state
decays mainly into instead of . If this relative branching
ratio is further confirmed by other experimental groups, we point out that the
identification of either as a state or more generally
as a state in the representation is probably
problematic. Instead, such an anomalous decay pattern strongly indicates
is a four quark state in the representation
with the quark content . We discuss its
partners in the same multiplet, and the similar four-quark states composed of a
bottom quark . Experimental searches of other members
especially those exotic ones are strongly called for
Loschmidt echo and fidelity decay near an exceptional point
Non-Hermitian classical and open quantum systems near an exceptional point
(EP) are known to undergo strong deviations in their dynamical behavior under
small perturbations or slow cycling of parameters as compared to Hermitian
systems. Such a strong sensitivity is at the heart of many interesting
phenomena and applications, such as the asymmetric breakdown of the adiabatic
theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions
and photonic catastrophe. Like for Hermitian systems, the sensitivity to
perturbations on the dynamical evolution can be captured by Loschmidt echo and
fidelity after imperfect time reversal or quench dynamics. Here we disclose a
rather counterintuitive phenomenon in certain non-Hermitian systems near an EP,
namely the deceleration (rather than acceleration) of the fidelity decay and
improved Loschmidt echo as compared to their Hermitian counterparts, despite
large (non-perturbative) deformation of the energy spectrum introduced by the
perturbations. This behavior is illustrated by considering the fidelity decay
and Loschmidt echo for the single-particle hopping dynamics on a tight-binding
lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi
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