We derive saddlepoint approximations for the distribution and density functions of the half-life estimated by OLS from autoregressive time-series models. Our results are used to prove that none of the integer-order moments of these half-life estimators exist. This provides an explanation for the very large estimates of persistency, and the extremely wide confidence intervals, that have been reported by various authors – for example in the empirical economics literature relating to purchasing power parity.

We derive saddlepoint approximations for the density and distribution functions of the half-life estimated by OLS from an AR(1) or AR(p) model. Our analytic results are used to prove that none of the integer-order moments of these half-life estimators exist. This provides an explanation for the unreasonably large estimates of persistency associated with the purchasing power parity “puzzle”, and it also explains the excessively wide confidence intervals reported in the empirical PPP literature.

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Universités d'Aix-Marseille II et III Document de Travail n°2011-07 Long-run relationships between international stock prices: further evidence from fractional cointegration tests