LARGE DEVIATION RESULTS FOR THE ESTIMATIONS OF COVARIANCE AND MEAN OF LINEAR STATIONARY PROCESSES

We consider the discrete time linear stationary process: X(t)=\sum_j=0^\infty a_j \varepsilon(t-j), \quad t=0, \pm 1, \pm 2, \cdots Where ε（t） is a \mathscrF_t-stationary ergodic martingale difference sequences. We assume a₀=1, \sum_j=0^\infty\left|a_j\right|<\infty and E\left\varepsilon^2(t) \mid \mathscrF_t-1\right=\sigma^2>0 a. s. Let the sample covariance function and the sample mean function of the prooess X （t） be respoectively: \hatr_N(k)=\frac1N \sum_t=1^N-k X(t) X(t+k)=\hatr_N(-k), \quad k=0,1,2, \cdots and \hatW_N=\frac1N \sum_t=0^N X(t) where N is an arbitrary positive integer. The aim of this paper is to derive largo deviation for the sample eovarianee function and thesample mean fuuetions.