AR and MA representation of partial autocorrelation functions, with applications

Details AR and MA representation of partial autocorrelation functions, with applications AR and MA representation of partial autocorrelation functions, with applications

2007-02-22

arxiv.org/abs/math/0702648v7

Mathematics

Spectral Theory

Published in Probability Theory and Related Fields

Scientific paper

10.1007/s00440-007-0074-1

We prove a representation of the partial autocorrelation function (PACF), or
the Verblunsky coefficients, of a stationary process in terms of the AR and MA
coefficients. We apply it to show the asymptotic behaviour of the PACF. We also
propose a new definition of short and long memory in terms of the PACF.

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