From: "Peter Hamer" <pgh@nortelnetworks.com>
Subject: Re: Help on non-integer derivatives
Date: Thu, 06 Jan 2000 16:49:33 +0000
To: Dave Rusin <rusin@math.niu.edu>
Summary: FARIMA and fractional derivatives

Dave Rusin wrote:

> Thanks. Could you say something about how
> > FARIMA = fractional auto-regressive integrated moving average?
> actually makes use of fractional derivatives?

I'm not sure if it's fractional derivatives or fractional integrals.
Either way its probably in terms of finite differences rather than
derivatives. I've not really got beyond a black-box understanding that
they can be [need to be] used for time series with long-range
dependency, where the time- series may well be fractal in nature.  eg see
http://www.amstat.org/publications/jasa/abstracts_97/sept/ling.htm
http://math.bu.edu/INDIVIDUAL/murad/methods/time_series/

My own interests have lead my down a multifractal wavelet model
path rather than using FARIMA models. [If nothing else last year
taught me a lot of new buzzwords.]

> I'm curious because as it
> turns out there are some real technical hurdles even coming up with
> a decent definition of them.

I'm not into fractional calculus myself, but was exposed to the
differential operator D a little at university -- way back in the 60s
so the memory isn't too fresh. In terms of D the definitions seem
fairly straightforward

(actually calculating them could be quite a different matter!).
http://mathworld.wolfram.com/DifferentialOperator.html
http://mathworld.wolfram.com/FractionalCalculus.html

What are the `real technical hurdles', if you can explain them simply?

Peter