The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study

This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR’s estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have the usual asymptotic chi-square distribution. This result is consistent with Ohanian’s finding. Furthermore, the derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk. Interestingly, it can also be shown that if the genuine variables of the model are stationary, the asymptotic distribution is still chi-square in spite of the inclusion of the random walk

Vertex operator approach for form factors of Belavin's (Z/nZ)(Z/nZ)-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. Free field representations of nonlocal tail operators are constructed for off diagonal matrix elements with respect to the ground state sectors. As a result, integral formulae for form factors of any local operators in the $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained, in principle.Comment: 24 pages, 4 figures, published in J. Phys. A: Math. Theor. 43 (2010) 085202. For the next thirty days from Feb 5 2010, the full text of the article will be completely free to access through our 'This Month's Papers' service (www.iop.org/journals/thismonth), helping you to benefit from maximum visibilit

Vector Autoregression and Causality

This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR’s) and Johansen-type error correction models (ECM’s) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate VAR systems is extended to the general case, thereby formally characterizing the circumstances when these Wald tests are asymptotically valid as chi-square criteria. Our results for inference from unrestricted levels VAR are not encouraging

Vector Autoregression and Causality: A Theoretical Overview and Simulation Study

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR’s) and Johansen-type error correction models (ECM’s). for VAR models the results for inference are not encouraging. The limit theory typically involves nonstandard distributions and nuisance parameters, and there is no sound statistical basis for testing causality in such a framework. Granger causality tests in ECM’s also suffer from nuisance parameter dependencies asymptotically and nonstandard limit theory. But, in spite of these difficulties Johansen-type ECM’s do offer a sound basis for empirical testing of the rank of the cointegration space and the rank of key submatrices that influence the asymptotics. In consequence, we recommend some operational procedures for conducting Granger causality tests in the important practical case of testing the causal effects of one variable on another group of variables and vice versa

Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the $A^{(1)}_{n-1}$ model. Correlation functions of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available at http://stacks.iop.org/1751-8121/42/16521

Quantum description for a chiral condensate disoriented in a certain direction in isospace

We derive a quantum state of the disoriented chiral condensate dynamically, considering small quantum fluctuations around a classical chiral condensate disoriented in a certain direction $\vec n$ in isospace. The obtained nonisosinglet quantum state has the characteristic features; (i) it has the form of the squeezed state, (ii) the state contains not only the component of pion quanta in the direction $\vec n$ but also the component in the perpendicular direction to $\vec n$ and (iii) the low momentum pions in the state violate the isospin symmetry. With the quantum state, we calculate the probability of the neutral fraction depending on the time and the pion's momentum, and find that the probability has an unfamiliar form. For the low momentum pions, the parametric resonance mechanism works with the result that the probability of the neutral fraction becomes the well known form approximately and that the charge fluctuation is small.Comment: 19 page

Analisis Pendapatan Masyarakat Melayu di Desa Pekantua Kecamatan Kempas Kabupaten Indragiri Hilir

Malay community in Pekantua Village still predominate that is 80%. geographically Pekantua Village resid in alongside river stream of Indragiri, Pekantua Village is one of the oldest village in Indragiri Hilir. The purpose of this research is to determine the income level of Malay community in Pekantua Village Kempas District Indragiri Hilir Regency. This research conducted by purposive sampling of 30 Malay community samples. The result showed that the income level of Malay community in Pekantua Village consists of father income, mother income, and child income. Father income who above regency minimum pay (UMK) Indragiri Hilir Regency going into effect in the year 2015 is Rp. 1.940.500,- as many as 19 respondents from 30 respondents (53,33%), who have income under regency minimum pay (UMK) as many as 11 respondents (36,66%). The main livelihood of father is rubber farmer, and secondary livelihood are ship worker, fishermen, trader, builder, and sand miner. Mother income who above regency minimum pay (UMK) as many as 2 respondents from 30 respondents (6,67%), who have income under regency minimum pay (UMK) as many as 12 respondents (40,00%). The livelihood of mother is farmer and trader. Child income who above regency minimum pay (UMK) as many as 1 respondents from 30 respondents (3.33%), who have income under regency minimum pay (UMK) as many as 6 respondents (20,00%), and who have not income as many as 23 respondents (76,66%). The livelihood of child is farmer, ship worker, trader

Parametric amplification with a friction in heavy ion collisions

We study the effects of the expansion of the system and the friction on the parametric amplification of mesonic fields in high energy heavy ion collisions within the linear $\sigma$ model . The equation of motion which is similar to Mathieu equation is derived to describe the time development of classical fields in the last stage of a heavy ion collision after the freezeout time. The enhanced mode is extracted analytically by comparison with Mathieu equation and the equation of motion is solved numerically to examine whether soft modes will be enhanced or not. It is found that the strong peak appears around 267 MeV in the pion transverse momentum distribution in cases with weak friction and high maximum temperature. This enhancement can be extracted by taking the ratio between different modes in the pion transverse momentum distribution.Comment: 10 pages, 9 figures LaTeX: appendix adde

Compound basis arising from the basic A1(1)A^{(1)}_{1}-module

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.Comment: 12 page

Dynamical Pion Production via Parametric Resonance from Disoriented Chiral Condensate

We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $\sigma$ oscillations, which may be appropriate for the late stage of nonequilibrium phase transition. It allows us to obtain an explicit quantum state of the produced pions and $\sigma$, the squeezed state of BCS type. Single particle distributions and two-pion correlation functions are computed within these approximations. The results obtained illuminate the characteristic features of multi-pion states produced through the parametric amplification mechanism. In particular, two-pion correlations of various charge combinations contain back-to-back correlations which cannot be masked by the identical particle interference effect.Comment: REVTEX 18 pages and 10 figure