Information theoretic results for circular distributions

The broad class of generalized von Mises (GvM) circular distributions has certain optimal properties with respect to information theoretic quantities. It is shown that, under constraints on the trigonometric moments, and using the Kullback–Leibler information as the measure, the closest circular distribution to any other is of the GvM form. The lower bounds for the Kullback–Leibler information in this situation are also provided. The same problem is also considered using a modified version of the Kullback–Leibler information. Finally, series expansions are given for the entropy and the normalizing constants of the GvM distribution.     

A new nonlinear unit root test with Fourier function

Abstract

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an exponential smooth threshold autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse and KSS tests.     

Exact factorization of the spectral density ann its application to wrf,castiilg and time series analysis

Let f be the spectral density function of a purely nondeterministic stationary stochastic process and be the optimal (canonical) fator of f. The role of the coefficients c_n and d_n (n ≥ 0) of φ and φ^?1 respectivey, in prediction, filtering and control theory is well-knwn. We show that the c_n's and d_n's can be obtained recursively in terms of the Fourier coefficients of log f. Also, recursive and updating formulae fr the kolmogorovwiener predictor similar to those Box-Jenkins are provided..     

A new nonparametric procedure designed for simulation studies

This paper demonstrates how certain statistics, computed from a sample of size n (from almost any distribution) may be simulated by using a sequence of substantially less than n random normal variates. Many statistics, θ, including almost all maximum likelihood estimates, can be expressed in terms of the sample trigonometric moments, STM. The STM are asymptotically multivariate normal with a mean vector and variance-covariance matrix easily expressible in terms of equally spaced characteristic function evaluations. Thus one only needs to know the Fourier transform or equivalently the characteristic function associated with elements of any moderate to large i. i. d. sample and have access to a normal random number generator to generate a sequence of STM with distributional properties almost identical to those of STM computed from that sample. These STM can in turn be used to compute the desired statistic θ.