In multivariate time series modelling, we are often led to investigate the existence of a relationship between two time series. Here, we generalize the procedure proposed by Haugh (1976) and extended by El Himdi and Roy (1997) for multivariate stationary ARMA time series to the case of...

In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite-order vector autoregressive (VAR(infinity)) series, which is an extension of Hong's [Biometrika...

We compare the performance of the inverse and ordinary (partial) autocorrelations for time series model identification. It is found that, both in terms of Bahadur's slope and Pitman's asymptotic relative efficiency, the inverse partial autocorrelations are more efficient than the ordinary...

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...

This paper considers estimation of ARMA models with time-varying coefficients. The ARMA parameters belong to d different regimes. The changes in regime occur at irregular time intervals. Consistency and asymptotic normality of least squares and quasi-generalized least squares estimators are...

We study the asymptotic behaviour of the least squares estimator, of the residual autocorrelations and of the Ljung-Box (or Box-Pierce) portmanteau test statistic for multiple autoregressive time series models with nonindependent innovations. Under mild assumptions, it is shown that the...