Estimating Markov-Switching ARMA Models with Extended Algorithms of Hamilton

This paper proposes two innovative algorithms to estimate a general class of N-state Markov-switching autoregressive moving-average (MS-ARMA) models with a sample of size T. To resolve the problem of NT possible routes induced by the presence of MA parameters, the first algorithm is built on Hamilton’s (1989) method and Gray’s (1996) idea of replacing the lagged error terms with their corresponding conditional expectations. We thus name it as the Hamilton-Gray (HG) algorithm. The second method refines the HG algorithm by recursively updating the conditional expectations of these errors and is named as the extended Hamilton-Gray (EHG) algorithm. The computational cost of both algorithms is very mild, because the implementation of these algorithms is very much similar to that of Hamilton (1989). The simulations show that the finite sample performance of the EHG algorithm is very satisfactory and is much better than that of the HG counterpart. We also apply the EHG algorithm to the issues of dating U.S. business cycles with the same real GNP data employed in Hamilton (1989). The turning points identified with the EHG algorithm resemble closely to those of the NBER’s Business Cycle Dating Committee and confirm the robustness of the findings in Hamilton (1989) about the effectiveness of Markov-switching models in dating U.S. business cycles.Markov-switching, ARMA process

Cryptanalysis and improvement of the quantum private comparison protocol based on Bell entangled states

Recently, Liu et al. [Commun. Theor. Phys. 57, 583, 2012] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party (TP). However, this study points out there is a fatal loophole in this protocol, i.e., TP can obtain all of the two participants secret inputs without being detected through making a specific Bell-basis measurement. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol, it also reduces the Bell states consumption and simplifies the steps in the protocol.Comment: 9 pages, 1 figur

Improved Deterministic N-To-One Joint Remote Preparation of an Arbitrary Qubit via EPR Pairs

Recently, Bich et al. (Int. J. Theor. Phys. 51: 2272, 2012) proposed two deterministic joint remote state preparation (JRSP) protocols of an arbitrary single-qubit state: one is for two preparers to remotely prepare for a receiver by using two Einstein-Podolsky-Rosen (ERP) pairs; the other is its generalized form in the case of arbitrary N>2 preparers via N ERP pairs. In this paper, Through reviewing and analyzing Bich et al.'s second protocols with N>2 preparers, we find that the success probability P_{suc}=1/4 < 1. In order to solve the problem, we firstly constructed two sets of projective measurement bases: the real-coefficient basis and the complex-coefficient one, and further proposed an improved deterministic N-to-one JRSP protocol for an arbitrary single-qubit state with unit success probability (i.e, P_{suc}=1). Morever, our protocol is also flexible and convenient, and it can be used in a practical network.Comment: 13 pages, 2 figures, two table

U-boson and the HyperCP exotic events

We show that the very light spin-1 gauge U-boson of the extra $U(1)'$ gauge model in the framework of the supersymmetric standard model extension can be a good candidate of the new light particle suggested by the HyperCP experiment. We demonstrate that the flavor changing neutral currents (FCNCs) for the HyperCP events in the decay of $\Sigma^{+}\to p \mu^{+} \mu^{-}$ can be generated at both tree and loop levels. In particular, we find that the loop induced $s\to d U$ transition due to the tensor-type interaction with the dimension-5 electric dipole operator plays a very important role on the FCNCs. Our explanation of the HyperCP data with the spin-1 U-boson is different from that based on a light pseudoscalar Higgs boson or sgoldstino in the literature. In particular, the U-boson involves a rich phenomenology in particle physics as well as cosmology.Comment: 12 pages, 2 figures, refs. added, final version to appear in PL

Edge Excitations in Fractional Chern Insulators

Recent theoretical works have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role to obtain a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagom\'{e}-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.Comment: 5 pages, 4 figures, 1 table, with Supplementary Materia