Suppose we are interested in forecasting a time series and, in addition to the time series data, we have data from many time series related to the one we want to forecast. Since building a dynamic multivariate model for the set of time series can be a complex task, it is important to measure in...

This article proposes pure significance tests for the absence of nonlinearity in cointegrating relationships. No assumption of the functional form of the nonlinearity is made. It is envisaged that the application of such tests could form the first step towards specifying a nonlinear...

We develop extensions of the Dickey-Fuller F-statistics for the joint null hypothesis of a unit root that allows for a break in the innovation variance. Our statistics are based on the modified generalized least squares (GLS) strategy outlined in Kim, Leybourne and Newbold [Journal of...

We investigate a new tool for measuring whiteness. We first introduce a quantity which has suitable properties for constructing a test for randomness. We provide the exact asymptotic power of our test. Finally, we experimentally assess the power and usefulness of our test. Copyright 2007 The...

We determine the form of spectral densities of multidimensional scalar processes which minimize a relative entropy under a finite number of general moment-type constraints. The obtained theoretical results are applied to spectral densities of weakly stationary processes under covariances,...

We demonstrate a reliable and computationally feasible method for determining whether a given threshold autoregression autoregressive conditional heteroscedastic (AR-ARCH) model is ergodic, and for determining which moments exist when it is ergodic. This method may be used to delineate the...

In this article, we study high moment partial sum processes based on residuals of a stationary autoregressive moving average (ARMA) model with known or unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the i.i.d....

In this article, we provide a spectral characterization for a real-valued discrete-time periodically correlated process, and then proceed on to establish a simulation procedure to simulate such a Gaussian process for a given spectral density. We also prove that the simulated process, at each...

We introduce a state-space representation for vector autoregressive moving-average models that enables maximum likelihood estimation using the EM algorithm. We obtain closed-form expressions for both the E- and M-steps; the former requires the Kalman filter and a fixed-interval smoother, and the...

This article introduces a family of 'generalized long-memory time series models', in which observations have a specified conditional distribution, given a latent Gaussian fractionally integrated autoregressive moving-average (ARFIMA) process. The observations may have discrete or continuous...