An information-geometrical foundation is established for the deformed exponential families of probability distributions. Two different types of geometrical structures, an invariant geometry and a flat geometry, are given to a manifold of a deformed exponential family. The two different...

This paper develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Lévy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a...

Weak convergence of partial sums and multilinear forms in independent random variables and linear processes to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and...

Structural break points in the First Division/English Premier League time series of competitive balance identify an Early Period, a Pre-World War II Period, a Post-War Period, and a Modern Period. The Early Period corresponds to technology diffusion (defense and tactics) along with important...

We provide a new framework for identifying timing. Our analysis focuses on the smoothed joint history of the fund with the benchmark. The approach is fully non-parametric. Therefore, it has the advantage of avoiding the misspecification problems so common in this literature. The test statistic...

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a...