Time series models with time dependent coefficients.

Summary In this thesis, we study the probabilistic and/or statistical properties of linear or non-linear time series models with time-dependent coefficients. The first part of the thesis is devoted to the statistics of ARMA models whose coefficients vary according to recurrent, but non-periodic events. The asymptotic properties (strong convergence and normality) of the least squares estimators are established. The special case of ARMA models with Markovian regime switching is then considered. The second part of the thesis studies the asymptotic influence of the time series mean correction on the least squares estimation of periodic ARMA models. In the last part of the thesis, we extend our research to bilinear models with periodic coefficients. The results obtained are regularly illustrated at finite distance using Monte Carlo experiments.