Please use a meaningful subject.
What you want is often called the eventual forecast function. For an
AR(1) it is beta^r for r steps ahead. The distribution of Y(t+tau) | Y(t)
= y* is in all good time-series books, certainly in those by Brockwell &
Davis. You can also get it from the arima.forecast function in S-PLUS.
On Wed, 25 Jun 2003, Leeds, Mark wrote:
> can anyone answer the following or know of a reference for
> the following type of question ?
>
> suppose i have an AR(1) model where the coefficient
> is Beta.
>
> so, the equation is y_t = mu + beta*y_t-1 + epsilon
>
> if the model is estimated with a daily frequency,
> so that is t is daily, are there formulas
> that exist for how many days it will take for
> y_t to "return" to its long run average
> when it at say y* at time t ?
>
> i imagine, if there is a formula, then it's a function
> of beta and the volatility of epsilon but i haven't seen one in any
> books
> that i'm familar with ? thanks.
>
> mark
>
--
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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