XCAP iPolyFitPredict

Originally Posted by Paul A. Griffin

XCAP_iPolyFitPredict:

Uses a fit to polynomials to create a least squares best fit for a given maximum degree. Extends the fit
forward in time for trading purposes. See reference [1] for more information.

Author: Paul A. Griffin
January 4, 2007
Extrema Capital, 2007

This indicator provides as output the least square best fit to a set of polynomials of maximum power (degree) using
discrete Legendre polynomials. This is accomplished by decomposing the time series into discrete Legendre polynomials
over the interval of orthogonality given by 2 * Width + 1 and discarding the polynomial fits degrees above some maximum degree.
The remaining smoothed series is continued forward in time by following the polynomial fit.

Some Comments:

In this indicator, we are displaying the least squares fit to a low degree set of polynomials and extending that fit
into the future. This as a tool to extend a low order trend into the future.

Some Plots:

All Charts: Daily chart with a width of 126 bars (126*2+1 = 253, about 1 trading year)

For @US (30 year US Treasury Bond Futures), and SPY roughly for year 2006

MaxDegrees: 1, 2, 3

ForwardExtension: 10

ShowLeadingEdge = TRUE

As you move forward along the time series, the fit is generated. What is displayed is the leading, rightmost bar, "[0]", for
each fit.

ShowPredictedEdge = TRUE

As you move forward along the time series, the fit is generated, and then a prediction is made.
What is displayed is the predicted, beyond the rightmost bar, "[-ForwardExtension]", for each fit.

ShowLastFit = TRUE

This displays the entire last fit for just the last bar on the chart, so you will only see an output on the last
2*Width + 1 bars of your chart. It will also display the polynomial extension of the fit forward in time to bar
[-ForwardExtension]

References:

[1] Legendre Polynomial Fits https://www.tradestation.com/Discuss...Topic_ID=58534

[2] Savitzky Golay https://www.tradestation.com/Discuss...Topic_ID=59250

[3] http://en.wikipedia.org/wiki/Legendre_polynomials

[4] Peter Seffen, "On Digital Smoothing Filters: A Brief Review of Closed Form Solutions and Two New Filter Approaches",
Circuits Systems Signal Process, Vol. 5, No 2, 1986

Note:
This indicator was written in EasyLanguage.
Please refer to your users manual for importation instructions.

Your comments and rating of this indicator is appreciated.

[aaa]

very interesting serie of Polynomials indic

what about the Polycycle indic ?

[Tams]

related indicators:

XCAP iPolyCycle
http://www.traderslaboratory.com/for...ycle-7072.html

XCAP IPolyFit
http://www.traderslaboratory.com/for...yfit-7039.html

[aaa]

They are much more information than on Tams' graph

First it looks like a Regression Line and then other thin angles lines appears + a kind of curved avg

I wish to have more info but noway to follow these links

[1] Legendre Polynomial Fits https://www.tradestation.com/Discuss...Topic_ID=58534

[2] Savitzky Golay https://www.tradestation.com/Discuss...Topic_ID=59250

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