XCAP IPolyFitPredict

[Tams 20]

XCAP iPolyFitPredict

 

 

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/Discussions/Topic.aspx?Topic_ID=58534

 

[2] Savitzky Golay https://www.tradestation.com/Discussions/Topic.aspx?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.

XCAP_iPolyFitPredict_(MultiCharts).pla

XCAP_iPolyFitPredict_(EasyLanguage).txt

Edited October 28, 2009 by Tams

[aaa 10]

very interesting serie of Polynomials indic

 

what about the Polycycle indic ?

[Tams 20]

related indicators:

 

XCAP iPolyCycle

http://www.traderslaboratory.com/forums/f46/xcap_ipolycycle-7072.html

 

XCAP IPolyFit

http://www.traderslaboratory.com/forums/f46/xcap-ipolyfit-7039.html

 

[aaa 10]

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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