The classical regular and partial autocorrelation functions are powerful
tools for stationary time series modelling and analysis. However, it is
increasingly recognized that many time series are not stationary and the use of
classical global autocorrelations can give misleading answers. This article
introduces two estimators of the local partial autocorrelation function and
establishes their asymptotic properties. The article then illustrates the use
of these new estimators on both simulated and real time series. The examples
clearly demonstrate the strong practical benefits of local estimators for time
series that exhibit nonstationarities.