Consider the partly linear regression model yi=xi'β+g(ti)+εi,1≤i≤n,where yi's are responses,xi=(xi1,xi2,…,xip)' and ti∈T are known and monradom design points,T is a compact set in the real line R,β=(β1,…βp）'is an unknown parameter vector,g(+)is an unknown function and {εi} is a linear process,i.e.,ei=∑j=0 ∞ψjei-j,,ψ0=1,∑j=0 ∞|ψj|<∞,where ej are i.i.d. random variables with zero mean and variance σe^2,Drawing upon B-spline estimation of g(+)and least squares estimation of β,we construct estimators of the gutocovariances of {εi}.The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {εi} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zeroco efficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process.
