Try fractionally integrated ARMA, ARFIMA. ARFIMA is said to
be "long memory" process.
Also note that financial time series are extremely
conditionally heteroskedastic. This is captured by ARCH
models (autoregressive conditional heteroskedasticity). Also
innovations have fat tailed distribution even after taking
into account conditional heteroskedasticity. This means a
lot of extreme observations (outliers).
-----------------------------
Alexander Tsyplakov
Novosibirsk State University
http://www.nsu.ru/ef/tsy/
Nilufer Pettersson-Arm <[EMAIL PROTECTED]> ����� �
���������:92n1f0$ji9$[EMAIL PROTECTED]
> I am trying to build an ARIMA model for the movements of
the returns of a
> stock. I have differentiated my data series once to make
it stationary.
> The autocorrelations and partial autocorrelations do not
show any clear
> pattern to indicate a model. I have tried all kinds of
low-order models,
> but they fit the data VERY poorly. However, if I
differentiate it three
> times or more, the fit gets better. But, what does this
mean? The series
> is stationary after the first differencing and should
require no further
> differencing. Is it that further differencing only
smoothes the curve out?
> Is it possible that a process like this cannot be modelled
with ARIMA?
>
> Any help would be greatly appreciated.
>
> Nilufer
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