Consider the partly linear regression model
$$
y_{i} = {x}'_{i} \beta + g{\left( {t_{i} } \right)} + \varepsilon _{i} ,\;\;{\kern 1pt} 1 \leqslant i \leqslant n
$$
, where *y*_{i}’s are
responses,
$$
x_{i} = {\left( {x_{{i1}} ,x_{{i2}} , \cdots ,x_{{ip}} } \right)}^{\prime } \;\;\;{\text{and}}\;\;\;t_{i} \in {\cal T}
$$
are known and nonrandom design points,
$$
{\cal T}
$$
is a compact
set in the real line
$$
{\cal R}
$$
, *β* =
(*β*_{1}, ··· , *β*_{p})'
is an unknown parameter vector, *g*(·) is an unknown function and
{*ε*_{i}} is a linear process,
i.e.,
$$
\varepsilon _{i} {\kern 1pt} = {\kern 1pt} {\sum\limits_{j = 0}^\infty {\psi _{j} e_{{i - j}} ,{\kern 1pt} \;\psi _{0} {\kern 1pt} = {\kern 1pt} 1,\;{\kern 1pt} {\sum\limits_{j = 0}^\infty {{\left| {\psi _{j} } \right|} < \infty } }} }
$$
, where
*e*_{j} are i.i.d. random variables with zero
mean and variance
$$
\sigma ^{2}_{e}
$$
. Drawing upon *B*-spline estimation of *g*(·) and
least squares estimation of *β*, we construct estimators of the
autocovariances of {*ε*_{i}}. 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 {*ε*_{i}} 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-zero coeffcients of the process. Moreover,
our result can be used to construct the asymptotically effcient
estimators for parameters in the ARMA error process.