Analysis of Models with Complex Roots on the Unit Circle
نویسندگان
چکیده
This paper deals with nonstationary autoregressive (AR) models with complex roots on the unit circle. We examine the asymptotic properties of the least squares estimators (LSEs) in the model. We also extend the model to the case where the error term follows a stationary linear process. We show that the limiting distribution of the LSE of the unit root parameter has a property comparable to that of the LSE in the standard nonstationary seasonal model with period two. Percent points and moments of the limiting distribution are computed by numerical integration.
منابع مشابه
Root Statistics of Random Polynomials with Bounded Mahler Measure
The Mahler measure of a polynomial is a measure of complexity formed by taking the modulus of the leading coefficient times the modulus of the product of its roots outside the unit circle. The roots of a real degree N polynomial chosen uniformly from the set of polynomials of Mahler measure at most 1 yields a Pfaffian point process on the complex plane. When N is large, with probability tending...
متن کاملAsymptotic Results for Random Polynomials on the Unit Circle
In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let {nk}k=1 be an infinite sequence of positive integers and let {zk}k=1 be a sequence of i.i.d. uniform distributed random variables on the unit circle. The above pair of sequences determine a sequence of ra...
متن کاملA Structural Organization of Modern English Multiple Complex-Compound
The article focuses on the factors that cause linear and vertical sentence extension of multiple complex-compound sentences used in English fictional literature. Considering the sentence structure as a combination of 2 Units – paratactic and hypotactic the authors define the structural peculiarities of paratactic and hypotactic units including the number of clauses and its bonds. The extension ...
متن کاملNewman Polynomials, Reducibility, and Roots on the Unit Circle
A length k Newman polynomial is any polynomial of the form za1 + · · ·+zak (where a1 < · · · < ak). Some Newman polynomials are reducible over the rationals, and some are not. Some Newman polynomials have roots on the unit circle, and some do not. Defining, in a natural way, what we mean by the “proportion” of length k Newman polynomials with a given property, we prove that • 1/4 of length 3 Ne...
متن کاملOn The Mean Convergence of Biharmonic Functions
Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...
متن کامل