Related papers: Moderate deviations for the Durbin-Watson statisti…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…
The purpose of this paper is to investigate the asymptotic behavior of the Durbin-Watson statistic for the stable $p-$order autoregressive process when the driven noise is given by a first-order autoregressive process. It is an extension of…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…
The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general $p$th-order bifurcating autoregressive processes, under…
In the present paper, we consider the linear autoregressive model in $\rr$, $$ X_{k,n}=\theta_n X_{k,n-1}+\xi_k, k=0,1,...,n, n\ge 1$$ where $\theta_n\in [0,1)$ is unknown, $(\xi_k)_{k\in\zz}$ is a sequence of centered i.i.d. r.v. valued in…
We are interested in the implications of a linearly autocorrelated driven noise on the asymptotic behavior of the usual least squares estimator in a stable autoregressive process. We show that the least squares estimator is not consistent…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control.…
In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.
In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…
In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…
In this article, we give explicit bounds on the Wasserstein and the Kolmogorov distances between random variables lying in the first chaos of the Poisson space and the standard Normal distribution, using the results proved by Last, Peccati…
Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large…
In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…
Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…