In this article we consider the problem of testing for the presence of a unit root against autoregressive alternatives. In this context we prove the asymptotic equivalence of the well-known (augmented) Dickey-Fuller test with a test based on an appropriate parametric modification of the...

A robust version of local linear regression smoothers augmented with variable bandwidths is investigated for dependent spatial processes. The (uniform) weak consistency as well as asymptotic normality for the local linear M-estimator (LLME) of the spatial regression function g(<b>x</b>) are established...

A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a...

We show that tests for a break in the persistence of a time series in the classical I(0)/I(1) framework have serious size distortions when the actual data-generating process (DGP) exhibits long-range dependencies. We prove that the limiting distribution of a CUSUM of squares-based test depends...

This article studies tests for assessing whether two stationary and independent time series have the same dynamics - specifically, whether the autocovariances of both series coincide at all lags. Frequency domain statistics previously proposed for this purpose are reviewed. A time domain...

We give a method for generation of periodically correlated and multivariate ARIMA models whose dynamic characteristics are partially or fully specified in terms of spectral poles and zeroes or their equivalents in the form of eigenvalues/eigenvectors of associated model matrices. Our method is...

This article considers the problem of selecting among competing nonlinear time series models by using complexity-penalized likelihood criteria. An extensive simulation study is undertaken to assess the small-sample performance of several popular criteria in selecting among nonlinear...

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear...

We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X_k = (&phiv; + b_k)X_k - 1 + e_k, where (&phiv;, omega-super-2, σ-super-2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |&phiv; + b_0| = 0 and show that σ-super-2...

We introduce a new class of autoregressive models for integer-valued time series using the rounding operator. Compared with classical INAR models based on the thinning operator, the new models have several advantages: simple innovation structure, autoregressive coefficients with arbitrary signs,...