The Yule-Walker estimator is commonly used in time-series analysis, as a simple way to estimate the coefficients of an autoregressive process. Under strong assumptions on the noise process, this estimator possesses the same asymptotic properties as the Gaussian maximum likelihood estimator....

Numerous time series admit weak autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher...

This paper considers GMM estimation of autoregressive processes. It is shown that, contrary to the case where the noise is independent, using high-order moments can provide subtantial efficiency gains for estimating the AR model when the noise is only uncorrelated.

In this article we consider multivariate ARMA models subject to Markov-switching. In this article we show that the local stationarity of the observed process is neither sufficient nor necessary to obtain the global stationarity. We derive stationarity conditions and we compute the autocovariance...

In this paper, we consider a GARCH equation where the coefficients depend on the state of a non-observed Markov chain. First we establish necessary and sufficient conditions ensuring the existence of a stationary solution. Next, in the case of ARCH regimes, we show that the maximum likelihood...

In this paper, we consider the problem of estimating Switching-regime GARCH Models. The likelihood being in general intractable, we propose an estimation method based on linear representations.

For the statistical analysis of the ARMA models, the standard method requires that the linear innovations are martingale differences. This assumption is not satisfied for ARMA representations of non-linear processes. In such a case the standard method tipically entails an underestimation of the...