The Granger Non-Causality Test in Cointegrated Vector Autoregressions

In general, Wald tests for the Granger non-causality in vector autoregressive (VAR) process are known to have non-standard asymptotic properties for cointegrated systems. However, that may have standard asymptotic properties depending on the rank of the submatrix of cointegration. In this paper, we propose a procedure for conducting Granger non-causality tests that are based on discrimination of these asymptotic properties. This paper also investigate the finite sample performance of our testing procedure, and compare the testing procedure with conventional causality tests in levels VARfs.Vector autoregression, Cointegration, Granger causality, Hypothesis testing

A Bias-Corrected Estimation for Dynamic Panel Models in Small Samples

This paper is concerned with the estimation of the autoregressive parameter of dynamic panel data models. We propose a bias-corrected GMM estimator whose bias is smaller than that of many existing GMM estimators. And we propose a small sample corrected estimator of the variance in order to reduce the size distortion of the Wald test. These estimators are easy to calculate and do not require preliminary estimates. The Monte Carlo experiments indicate that in terms of both bias and size distortion, the bias corrected estimator out performs Blundell and Bond's (1998) system estimator even when using Windmeijer's (2005) correction of the estimated variance of the system estimator.Generalized method of moments, bias correction, panel data

On the power of alternation on reversal-bounded alternating Turing machines with a restriction

AbstractWhether or not there is a difference of the power among alternating Turing machines with a bounded number of alternations is one of the most important problems in the field of computer science. This paper presents the following result: Let R(n) be a space and reversal constructible function. Then, for any k ⩾ 1, we obtain that the class of languages accepted by off-line 1-tape rσk machines running in reversal O(R(n)) is equal to the class of languages accepted by off-line 1-tape σ1 machines running in reversal O(R(n)). An off-line 1-tape σk machine M is called an off-line 1-tape rσk machine if M always limits the non-blank part of the work-tape to at most O(R(n) log n) when making an alternation between universal and existential states during the computation

Optical Gravitational Wave Antenna with Increased Power Handling Capability

Fundamental sensitivity of an optical interferometric gravitational wave detector increases with increase of the optical power which, in turn, limited because of the opto-mechanical parametric instabilities of the interferometer. We propose to optimize geometrical shape of the mirrors of the detector to reduce the diffraction-limited finesse of unessential optical modes of the interferometer resulting in increase of the threshold of the opto-mechanical instabilities and subsequent increase of the measurement sensitivity. Utilizing parameters of the LIGO interferometer we found that the proposed technique allows constructing a Fabry-Perot interferometer with round trip diffraction loss of the fundamental mode not exceeding $5$~ppm, whereas the loss of the first dipole as well as the other high order modes exceed $1,000$~ppm and $8,000$~ppm, respectively. The optimization comes at the price of tighter tolerances on the mirror tilt stability, but does not result in a significant modification of the optical beam profile and does not require changes in the the gravity detector read-out system. The cavity with proposed mirrors is also stable with respect to the slight modification of the mirror shape.Comment: 5 pages, 4 figure

On fundamental diffraction limitation of finesse of a Fabry-Perot cavity

We perform a theoretical study of finesse limitations of a Fabry-Perot (FP) cavity occurring due to finite size, asymmetry, as well as imperfections of the cavity mirrors. A method of numerical simulations of the eigenvalue problem applicable for both the fundamental and high order cavity modes is suggested. Using this technique we find spatial profile of the modes and their round-trip diffraction loss. The results of the numerical simulations and analytical calculations are nearly identical when we consider a conventional FP cavity. The proposed numerical technique has much broader applicability range and is valid for any FP cavity with arbitrary non-spherical mirrors which have cylindrical symmetry but disturbed in an asymmetric way, for example, by tilt or roughness of their mirrors.Comment: 15 pages, 10 figure

Cointegration, Integration, and Long-Term Forcasting

It is widely believed that taking cointegration and integration into consideration is useful in constructing long-term forecasts for cointegrated processes. This paper shows that imposing neither cointegration nor integration leads to superior long-term forecasts.Forecasting, Cointegration, Integration

Forcasting in large cointegrated processes

It is widely recognized that taking cointegration relationships into consideration is useful in forecasting cointegrated processes. However, there are a few practical problems when forecasting large cointegrated processes using the well-known vector error correction model. First, it is hard to identify the cointegration rank in large models. Second, since the number of parameters to be estimated tends to be large relative to the sample size in large models, estimators will have large standard errors, and so will forecasts. The purpose of the present paper is to propose a new procedure for forecasting large cointegrated processes, which is free from the above problems. In our Monte Carlo experiment, we find that our forecast gains accuracy when we work with a larger model as long as the ratio of the cointegration rank to the number of variables in the process is high.Forcasting, Cointegration, Large Models

Effects of chemical composition and stereoregularity on phase-transition behaviors of aqueous solutions of copolymers composed of N-isopropylacrylamide and N-n-propylacrylamide

Radical copolymerizations of N-isopropylacrylamide (NIPAAm) and N-n-propylacrylamide (NNPAAm) in various ratios were carried out in toluene at –40 °C in the presence of 3-methyl-3-pentanol to prepare syndiotactic copolymers with racemo dyad contents of ca. 70%. It was revealed that copolymers containing more than 92.5 mol% NNPAAm units exhibited large phase-transition hysteresis of their aqueous solutions. Sequence analysis suggested that intramolecular hydrogen-bonding of contiguous NNPAAm units in syndiotactic stereosequences in the dehydrated state were responsible for induction of the large hysteresis