Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

By Randal Douc, Eric Moulines, Tobias Rydén. 2004

261 citations recorded by the source corpus.

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b8861318e3e4c36a73505eb8c915ecd0d888076e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Asymptotic properties of MLE for partially observed fractional diffusion system (2010, background): “Let us mention the papers [20, 1, 8, 5, 20, 21, 7, 15, 17] where the consistency and asymptotic normality of the Maximum Likelihood Estimator (MLE) has been discussed.”
The ACR Model: A Multivariate Dynamic Mixture Autoregression (2008, unknown): “5 Trading costs imply a nonlinear stationary process for the real exchange rate, as stressed in the theoretical models by Dumas (1992), Sercu, Uppal, and Van Hulle (1995) or Berka (2004), from which it follows that international arbitrage takes place if and only if the international price differenti”
An autoregressive model with time‐varying coefficients for wind fields (2006, methodology): “and assumptions which warrant consistency and asymptotic normality of MLE in MS-AR models with compact, not necessary finite, hidden state space S can be found in Douc et al. (2004). It would be beyond the scope of this paper to show that the MS-AR model proposed in section 2 verifies these assumpti”
Statistical inference for dynamical systems: A review (2012, background): “A few recent papers [42, 43, 46, 74] show asymptotic normality of the estimates of HMMs under increasingly general conditions.”