This paper reports on an extensive Monte Carlo study of seven residual-based tests of the hypothesis of no cointegration. Critical values and the power of the tests under the alternative of fractional cointegration are simulated and compared. It turns out that the Phillips-Perron t-test when applied to regression residuals is more powerful than Geweke-Porter-Hudak tests and the Augmented Dickey...

The n × n Brualdi-Li matrix Bn has recently been shown to have maximal Perron value (spectral radius) ρ among all tournament matrices of even order n, thus settling the conjecture by the same name. This renews our interest in estimating ρ and motivates us to study the Perron eigenvector x of Bn, which is normalized to have 1-norm equal to one. It follows that x minimizes the 2-norm among all Pe...

The transition matrix, which characterizes a discrete time homogeneous Markov chain, is a stochastic matrix. A stochastic matrix is a special nonnegative matrix with each row summing up to 1. In this paper, we focus on the computation of the stationary distribution of a transition matrix from the viewpoint of the Perron vector of a nonnegative matrix, based on which an algorithm for the station...

We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ -finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius-Perron semigroup of linear operators is C0-continuous in the space Lμ(X). We also give a geometrical c...

In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using KarhunenLoève (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty ev...

Koopman and Perron–Frobenius operators are linear operators that encapsulate dynamics of nonlinear dynamical systems without loss of information. This is accomplished by embedding the dynamics into a larger infinite-dimensional space where the focus of study is shifted from trajectory curves to measurement functions evaluated along trajectories and densities of trajectories evolving in time. Op...

CHANCHAN, PRAKASH. An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. (Under the direction of Carl D. Meyer.) We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz’s formula with a special inverse iteration algorithm discussed in [10, Linear Algebr...

We use the natural invariant density of map and Perron–Frobenius operator to analytically evaluate statistical properties for chaotic intermittency. This study can be understood as an improvement previous ones because it does not introduce assumptions about reinjection probability function in laminar interval or at pre-reinjection points. To validate new theoretical equations, we a symmetric no...

We provide a proof for a Perron-type theorem on the principal eigenvalue of nonsymmetric elliptic operators based on the strong maximum principle. This proof is modeled after a variational proof of Perron’s theorem for matrices with positive entries that does not appeal to Perron-Frobenius theory.