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 Electronic Journal of Probability > Vol. 4 (1999) > Paper 8 open journal systems 


Moderate deviations for stable Markov chains and regression models

Julien Worms, Universit'e de Marne La Vall'ee


Abstract
We prove moderate deviations principles for
  1. unbounded additive functionals of the form $S_n = sum_{j=1}^{n} g(X^{(p)}_{j-1})$, where $(X_n)_{ninbN}$ is a stable $bR^d$-valued functional autoregressive model of order $p$ with white noise and stationary distribution $mu$, and $g$ is an $bR^q$-valued Lipschitz function of order $(r,s)$;
  2. the error of the least squares estimator (LSE) of the matrix $theta$ in an $bR^d$-valued regression model $X_n = theta^t phi_{n-1} + epsilon_n$, where $(epsilon_n)$ is a generalized gaussian noise.
We apply these results to study the error of the LSE for a stable $bR^d$-valued linear autoregressive model of order $p$.


Full text: PDF

Pages: 1-28

Published on: April 16, 1999
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Electronic Journal of Probability. ISSN: 1083-6489