On Sun, 25 Apr 2004, Leeds, Mark wrote:
> if one has built an AR(1) model where the
> autoregressive parameter is less than
> 1, does anyone know of a book that derives
> the time till the level reverts back to it's original
It never does! The predictions decay geometrically at rate \phi (the
AR(1) parameter), but the level is a discrete-time continuous-value
stochastic process which therefore never hits any givne value.
> level. I think this often referred to as the half life
> of the model in the literature.
I think the `half life' is the time T for predictions to halve, that
is \phi^T = 0.5, T = -1/log_2 \phi. But surely the place to look is `the
literature' which defines this? (AFAIK, that is not the time series
literature.)
--
Brian D. Ripley, ripley@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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