This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time-reversible. Our approach is based on a simple index of the deviation from zero of the median of the one-dimensional marginal law of differenced data. An attractive feature of...

This article considers the problem of detecting break points for a nonstationary time series. Specifically, the time series is assumed to follow a parametric nonlinear time-series model in which the parameters may change values at fixed times. In this formulation, the number and locations of the...

We establish asymptotic normality and consistency for rank-based estimators of autoregressive-moving average model parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given by L.A. Jaeckel [Ann. Math. Stat. Vol. 43 (1972) 1449-1458]....

This article considers a mean zero stationary first-order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter rho_n is very near to one in the sense that 1 - rho_n =...

The aim of this article is to give a complete description of the spectral measure of periodic autoregressive moving-average (PARMA) system in terms of its coefficients. In the analysis we use the spectral theory of strongly harmonizable sequences presented in Hurd [Journal of Multivariate...

In this article, we study and compare the properties of several bootstrap unit-root tests recently proposed in the literature. The tests are Dickey-Fuller (DF) or Augmented DF, based either on residuals from an autoregression and the use of the block bootstrap or on first-differenced data and...

The analysis of liquidity in financial markets is generally performed by means of the dynamics of the observed intertrade durations (possibly weighted by price or volume). Various dynamic models for duration data have been considered in the literature, such as the Autoregressive Conditional...

The portmanteau statistic is based on the first m-residual autocorrelations, and is used for diagnostic checks on the adequacy of fit of a model. In this article, we propose a modified portmanteau statistic with a correction term that allows for the use of small values of m for the chi-squared...

Locally stationary processes are non-stationary stochastic processes the second-order structure of which varies smoothly over time. In this paper, we develop a method to bootstrap the local periodogram of a locally stationary process. Our method generates pseudo local periodogram ordinates by...

We evaluate the performance of several specification tests for Markov regime-switching time-series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung-Box tests based on both the generalized residual and a standard-normal residual...