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In this manuscript, we discuss a class of difference-based estimators of theautocovariance structure in a semiparametric regression model where the signalis discontinuous and the errors are serially correlated. The signal in thismodel consists of a sum of the function with jumps and an identifiable smoothfunction. A simpler form of this model has been considered earlier under thename of Nonparametric Jump Regression (NJRM). The estimators proposed allow usto bypass a complicated problem of prior estimation of the mean signal in sucha model. We provide finite-sample expressions for biases and variance of theproposed estimators when the errors are Gaussian. Gaussianity in the above isonly needed to provide explicit closed form expressions for biases andvariances of our estimators. Moreover, we observe that the mean squared errorof the proposed variance estimator does not depend on either the unknown smoothfunction that is a part of the mean signal nor on the values of differencesequence coefficients. Our approach also suggests sufficient conditions for$\sqrt{n}-$ consistency of the proposed estimators.

ACF estimation via difference schemes for a semiparametric model with m-dependent errors