This article studies the asymptotic properties of the discrete Fourier transforms (DFT) and the periodogram of a stationary long-memory time series over different epochs. The main theoretical result is a novel bound for the covariance of the DFT ordinates evaluated on two distinct epochs, which...

In practice, it is often impossible to assess the validity of the smoothness assumptions crucial to standard tests for singularities in the spectrum. We therefore propose new tests which are completely insensitive to sharp peaks in the absolutely continuous part of the spectrum. Using Neyman...

This article considers GARCH(1,1) models in which the time-varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive...

A general and flexible framework for the wavelet-based decompositions of stationary time series in discrete time, called adaptive wavelet decompositions (AWDs), is introduced. It is shown that several particular AWDs can be constructed with the aim of providing decomposition (approximation and...

Perron and Yabu (2009a) consider the problem of testing for a break occurring at an unknown date in the trend function of a univariate time series when the noise component can be either stationary or integrated. This article extends their work by proposing a sequential test that allows one to...

In this article, we propose new tests for threshold cointegration using an autoregressive distributed lag (ADL) model. The indicators in the threshold model can adopt either a nonstationary or stationary threshold variable. The cointegrating vector is not prespecified in this article. We adopt a...

This article proposes a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by Sul et al. (2005) to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of...

In this article, asymptotic theories for nonparametric methods are studied when they are applied to real-time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real-time random variables indexed...

A univariate first-order stochastic cycle can be represented as an element of a bivariate first-order vector autoregressive process, or VAR(1), where the transition matrix is associated with a rotation along a circle in the plane, and the reduced form is ARMA(2,1). This paper generalizes this...