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Strategies & Market Trends : Waiting for the big Kahuna

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To: Real Man who wrote (56777)	2/19/2002 1:48:43 AM
From: Moominoid	Read Replies (1) of 94695

A standard random walk (Hurst=0.5) can have a trend too as can a deterministic process with noise. But in the case of the random walk the trend has to be constant in one direction. And that seems unlikely over the very long term. An I(2) process (seems to be Hurst=1) is very smooth and has a variable trend - should be easy to project over a few periods. The practice of taking moving averages of stocks seems to be an effort to extract an I(2) like process and a stationary noise, both of which are more predictable than a random walk. The trouble with I(2) is that in theory past increments or innovations have increasingly powerful effects over time. This seems unlikely. So the fractionally integrated model with 0<Hurst<1 looks very attractive. I fractionally differenced the first difference of the NDX using 250 periods in filter (theoretically it should have infinite lags) and it did reduce the number of significant lags I got in ARMA models. Integration order was around 1.25. Stronger differencing seemed to lead to more lags again - i.e. over differencing. Probably I need more data and a longer truncation to get really good results - i.e white noise. The question is if you could use the fractional integrator to make forecasts? My technique currently relies on the ARMA model fitted to the first difference (and some other ideas). But if we had the true the fractional difference nothing would be significant in an ARMA model. But the forecasting model would be very simple - fractionally difference the past data and then run the integrator over that and forward iteratively to forecast. Mandelbrot hints that it wouldn't work though..... PS Is the Mandelbrot book worth getting? I just have the 1982 Fractal Geometry of Nature. David

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