  The class of autoregressive (AR) processes is extensively used to model
temporal dependence in observed time series. Such models are easily available
and routinely fitted using freely available statistical software like R. A
potential caveat in analyzing short time series is that commonly applied
estimators for the coefficients of AR processes are severely biased. This paper
suggests a model-based approach for bias correction of well-known estimators
for the coefficients of first and second-order stationary AR processes, taking
the sampling distribution of the original estimator into account. This is
achieved by modeling the relationship between the true and estimated AR
coefficients using weighted orthogonal polynomial regression, fitted to a huge
number of simulations. The finite-sample distributions of the new estimators
are approximated using transformations of skew-normal densities and their
properties are demonstrated by simulations and in the analysis of a real
ecological data set. The new estimators are easily available in our
accompanying R-package ARbiascorrect for time series of length n = 10, 11, ...
, 50, where original estimates are found using exact or conditional maximum
likelihood, Burg's method or the Yule-Walker equations.
