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 Statistics , 2015, Abstract: The paper studies Non-Stationary Dynamic Factor Models such that: (1) the factors $\mathbf F_t$ are $I(1)$ and singular, i.e. $\mathbf F_t$ has dimension $r$ and is driven by a $q$-dimensional white noise, the common shocks, with $q < r$, (2) the idiosyncratic components are $I(1)$. We show that $\mathbf F_t$ is driven by $r-c$ permanent shocks, where $c$ is the cointegration rank of $\mathbf F_t$, and $q-(r-c)  Statistics , 2014, Abstract: In this work we deal with the problem of fitting an error density to the goodness-of-fit test of the errors in nonlinear autoregressive time series models with stationary$\alpha$-mixing error terms. The test statistic is based on the integrated squared error of the nonparametric error density estimate and the null error density. By deriving the asymptotic normality of test statistics in these models, we extend the result of Cheng and Sun (Statist. Probab. Lett. \textbf{78}, 1(2008), 50-59) in the model with i.i.d error terms to the more general case.  Statistics , 2015, Abstract: In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale methods, we establish the moderate deviations for the least squares estimators of the regressor and error, which can be applied to understand the near-integrated second order autoregressive processes. As an application, we obtain the moderate deviations for the Durbin-Watson statistic.  Statistics , 2011, Abstract: Consider an autoregressive model with measurement error: we observe$Z_i=X_i+\epsilon_i$, where$X_i$is a stationary solution of the equation$X_i=f_{\theta^0}(X_{i-1})+\xi_i$. The regression function$f_{\theta^0}$is known up to a finite dimensional parameter$\theta^0$. The distributions of$X_0$and$\xi_1$are unknown whereas the distribution of$\epsilon_1$is completely known. We want to estimate the parameter$\theta^0$by using the observations$Z_0,..,Z_n$. We propose an estimation procedure based on a modified least square criterion involving a weight function$w$, to be suitably chosen. We give upper bounds for the risk of the estimator, which depend on the smoothness of the errors density$f_\epsilon$and on the smoothness properties of$w f_\theta\$.