Contribution to the identification of time series models.

Summary This doctoral thesis is divided into two parts dealing with identification and selection problems in econometrics. We study the following topics: (1) the problem of identifying time series models using autocorrelation, partial autocorrelation, inverse autocorrelation and inverse partial autocorrelation functions. (2) the estimation of the inverse autocorrelation function in the framework of nonlinear time series. In a first part, we consider the problem of identifying time series models using the above mentioned autocorrelation functions. We construct statistical tests based on empirical estimators of these functions and study their asymptotic distribution. Using the Bahadur and Pitman approach, we compare the performance of these autocorrelation functions in detecting the order of a moving average and an autoregressive model. Then, we identify the inverse process of an ARMA model and study its probabilistic properties. Finally, we characterize the temporal reversibility using the dual and inverse processes. The second part is devoted to the estimation of the inverse autocorrelation function in the framework of nonlinear processes. Under certain regularity conditions, we study the asymptotic properties of the empirical inverse autocorrelations for a stationary and strongly mixing process. We obtain the convergence and the asymptotic normality of the estimators. Next, we consider the case of a linear process generated by a white noise of GARCH type. We obtain an explicit formula for the asymptotic autocovariance matrix. Using examples, we show that the standard formula for this matrix is not valid when the process generating the data is nonlinear. Finally, we apply the previous results to show the asymptotic normality of estimators of the parameters of a weak moving average. Our results are illustrated by experiments.