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 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.

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 (i.i.d. or martingale difference), this estimator possesses the same asymptotic properties as the Gaussian...

The classical definition of GARCH-type processes rely on strong assumptions on the first two conditional moments. The common practice in empirical studies, however, has been to test for GARCH by detecting serial correlations in the squared regression errors. This can be problematic since such...

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...

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...