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Someone Wrote.....
"Might it be possible to somehow extrapolate the latest cycle from a shifted indicator into today's data? Has anyone done any work on this concept? "
I have done extensive forecasting work using Hurst's Centered and Inverse Moving Averages. I have attempted these forecasts using multiple regression and ARIMA models with little success. However, the problem I discovered, which is well documented in other readings, i.e., Channels & Cycles: A Tribute to J.M. Hurst by Brian Millard (a good book by the way), is that you cannot arbitrarily choose any length moving average to shift. If you do, your choice could be completely out of phase with the dominant cycle and market. This of course can cause financial disaster. What you must first do is develop an approach that allows you to isolate and identify the current dominant cycle in the time series under investigation.
To select the dominant cycle you could rely on Fourier analysis or John Ehler's MESA, or you could perform a decomposition of the time series (stocks, futures, mutual funds, etc.). Basic theory suggests a time series is comprised of four components, namely,
Trend
Seasonal
Cyclical
Random
You can start by detrending the series. There are a number of approaches that can be used, e.g., an Inverse Moving Average (Close - Centered Moving Average), some momentum function, etc. However, the selection of the look back period is the most critical choice to make at this point. After detrending, you are left with a new time series that only has the Seasonal, Cyclical and Random components. Next, if you are ready for more math, you can remove the seasonal component. Most basic forecasting or Econometric texts can give you guidelines on isolating and removing seasonal variations in a time series. If you make it to this point, subtract the seasonal component from the detrended series and you are left with the Cyclical plus Random components.
I hope this is enough to stimulate some new thought and appreciation to the problem your trying to solve. Like you, I hope others can contribute to the dialog.
James
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