Asymptotic statistics of some time series with memory.

Summary This thesis is devoted to the asymptotic inferential statistics of different noise-driven time series models with memory. In these models, the least squares estimator is not consistent and we consider alternative estimators. We start by studying the asymptotic properties of the maximum likelihood estimator of the autoregression coefficient in an autoregressive process driven by stationary Gaussian noise. We then present a statistical procedure to detect a regime shift in this model based on the classical case driven by strong white noise. We then discuss an autoregressive model where the coefficients are random and have a short memory. Here again the least squares estimator is not consistent and we correct the estimation in order to correctly estimate the model parameters. Finally we study a new joint estimator of the Hurst exponent and the variance in a high frequency fractional Gaussian noise whose qualities are comparable to maximum likelihood.