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Working Papers
 Nth Order Fading Memory Polynomial System v2
The nth Order Fading Memory Polynomial Short Term & Intraday System & Indicator. This package contains the advanced mathematical technique and noise filter called the Nth order fading memory polynomial (FADM). It is called fading memory because all of the an coefficients of the polynomial are updated recursively at each bar. Updated recursively means that the coefficients are a function of the coefficients of the previous bar and the squared error between the current bar and the projected polynomial. Thus the coefficients change more smoothly with each new bar than the fixed memory polynomial. This advanced mathematical technique is currently used in today's space-age missile and satellites applications and is applied here to stock and commodity trading.

The Nth Order Fading Memory Polynomial System v2

With this mathematical technique the price series is modeled using an nth order polynomial of the form:
price(t) = a0(t)+a1(t)*t+a2(t)*t2+a3(t)*t3+a4(t)*t4+...+an(t)*tn
Where all the an(t) coefficients are updated recursively with each new price bar. Very fast efficient algorithms compute the polynomial coefficients at each new price bar and give the polynomial's 1 day ahead prediction. The system follows the 1 day ahead generated curve and issues buy and sell signals based upon the curve turning up or down by a fixed percentage from a curve bottom or top.

These type of polynomial systems are best illustrated in my articles in the Stocks & Commodities June 2002 issue entitled "Trading IBM Intraday", in the Futures August 2000 issue entitled "Making Money From Memories"and in my Stocks & Commodities December 1998 issue entitled "The Yen, Recursed" (see papers page). Any fading memory polynomial order up to the 6th polynomial power can be used. In the manual, the Nth Order Fading Memory Polynomial System is applied to daily bars of the Japanese Yen futures, daily bars of the US6% Bond futures, and 1 min bars of the S&P500 E-mini futures. The Daily data is walk forward tested on 10 years of daily data and the E-mini is walk forward tested on more than 2 years of 1 min bars.

See Tables below for application of Walk Forward Out-Of-Sample Performance of 1 min Intraday bars on the S&P E-Mini futures and the Daily Bars on the Japanese Yen and CBT Bond futures. Please note performance values do not include slippage or commissions and that past performance is no guarantee of future results.

Product Description

All systems are orientated to short term trading in all bar ranges (1 tic, 1 min, 5min, etc., daily) and with any tradable price series. Each Daily Bar system is walk forward tested on 10 years of daily data on a continuous futures contract. The intraday 1min bar FADM system is walk forward tested on more than 74 weeks of 1min bars. The FADM can also be used on stock, options, and mutual fund data. Any or all of the systems can be combined using the functions described below.

All of the EasyLanguage™ system and indicator codes on disk are directly importable into TradeStation™ 2000i, 7/8 and are fully disclosed. There are no locks of any kind on the EasyLanguage source code. The C++ DLL code is not disclosed. The Input parameters to the system and indicator are changeable and optimizable so that the user can develop his own parameter set on his price series and time frame of interest. Although the system results will give parameters for the futures the system was tested on, the user can easily use these systems on any tradable or on any time frame.

The accompanying manual consists of:
  • A short tutorial on the details of performing walk forward optimization with out-of-sample testing using TradeStation
  • How I look for the "best" parameters in an optimization run.
  • A complete description of the system and it's input parameters.
  • The walk forward optimization method used and a table of the walk forward results for the system.
  • The parameter test ranges for each tradable used.
  • How to set the system and indicators up on TradeStation.
  • A Easylanguage system code printout.
  • A TradeStation chart printout of the system and its associated indicator with the out-of-sample period system buy & sell signals displayed on the chart.
  • Performance Summaries for the total time period and the out-of sample segments.
  • Special $Gain-$Drawdown per contract for each trade, trade by trade Summaries for the entire period.

The FADM Strategy includes the following Input Parameters:

  • Mark Mark=0 means the position is not marked to the market on the last bar of chart. Mark=1 means it is. Set Mark equal to zero if XTime not equal to zero.
  • Degree The Fading Memory polynomial order: 1=Straight Line, 2=quadratic, etc. Maximum=6.
  • NBars α is expressed in bars. α=2/(1+NBars). If NBars is set to zero then alpha used below.
  • alpha If not zero this value overrides NBars and sets the exponential decay constant directly
  • pctup The percent amount the FADM curve has to move up from a previous low while short in order to issue a buy signal. 9999 deactivates this condition.
  • pctdn The percent amount the FADM curve has to decrease from a previous prior high of the curve while long in order to issue a sell signal. 9999 deactivates this condition.
  • pctjup The percent amount the FADM curve has to increase from 2 bars ago to issue a buy signal. 9999=Not Used.
  • pctjdn The percent amount the FADM curve has to decrease from 2 bars ago to issue a sell signal. 9999=Not Used.
  • XOpn For Intraday bars only. Enter position after the open after XOpn price bars have passed. An input value of 0 means ignore this parameter.
  • Xtime Used only for Intraday bars. Exit position before or at the close at Xtime (1615). 0 = ignore
  • XonCls If value is 0 then enter/exit position at market. If 1 then enter/exit position on bar close.
  • prc This input can be any function of price such as (h+l)/2, c of data2, (h+l+c)/3 etc.

The input parameter XOpn allows the system to not open any trades until XOpn bars have past. This allows the system to avoid open whipsaw trades. The input parameter XTime allows the system to close any open trade before the close. For instance XTime would allow you to close all open trades at 4:05 ET so you would not be caught by the closing rush. The system has its exact duplicate in indicator form which is displayable on the price chart and in the charts printout, so that the user can visually see how the buy and sell signals occur.

The Nth Order Fading Memory Polynomial System package consists of a manual with tutorial as described above, System & Indicator els files, and a DLL file. This stand alone system is offered through Meyers Analytics L.L.C. for $395 plus shipping. Shipping via Email consists of the Manual in Adobe PDF format, ELS/ELD file and DLL file.

How To Order
To order online click Order Online. To order via Fax or mail using a Visa or Master Card please fill out the order form on the Order Form page and Fax it to the telephone number on the order form or mail it to the address on the order form. If you would like to talk to me about the product, please call me at (312) 280-1687 M-F 12pm to 5pm CST. All E-mail queries can be sent to info@meyersanalytics.com.

Thank you for your Interest....Dennis Meyers
4th Order Fading Memory Polynomial System using E-Mini 1min Bars
S&P E-mini Futures 1min Bars Out-Of-Sample Performance
Hypothetical Out-Of-Sample past performance is no guarantee of future results
OS Week = Out-Of-Sample Week Ending
$TNP=$ Total Net Profits For Week
OS
Week		 OS
Week
$TNP		 OS #
Trds		 OS
Week		 OS
Week
$TNP		 OS #
Trds		 OS
Week		 OS
Week
$TNP		 OS #
Trds		 OS
Week		 OS
Week
$TNP		 OS #
Trds
11/02/01 $1,000 13 11/09/01 $875 14 11/16/01 $263 10 11/23/01 $588 7
11/30/01 $88 10 12/07/01 $413 11 12/14/01 $113 11 12/21/01 $138 8
12/28/01 ($175) 3 01/04/02 ($63) 7 01/11/02 $288 8 01/18/02 $38 9
01/25/02 $50 6 02/01/02 $3,000 7 02/08/02 $38 16 02/15/02 $1,113 6
02/22/02 $2,050 7 03/01/02 $1,613 11 03/08/02 $25 9 03/15/02 ($88) 9
03/22/02 $113 9 03/29/02 ($213) 8 04/05/02 $375 9 04/12/02 ($13) 17
04/19/02($1,288) 11 04/26/02 $525 12 05/03/02 $1,475 9 05/10/02 $2,500 11
05/17/02 ($1,200) 11 05/24/02 $388 8 05/31/02 ($250) 8 06/07/02 ($125) 12
06/14/02 $938 11 06/21/02 $1,375 10 06/28/02 $1,988 14 07/05/02 $2,463 10
07/12/02 ($1,675) 23 07/19/02 $4,013 20 07/26/02 $188 58 08/02/02 $3,313 14
08/09/02 $2,513 15 08/16/02 ($288) 16 08/23/02 $1,425 10 08/30/02 $200 15
09/06/02 ($488) 11 09/13/02 $150 13 09/20/02 $250 14 09/27/02 $1,325 16
10/04/02 $1,325 26 10/11/02 $188 30 10/18/02 $238 13 10/25/02 $13 15
11/01/02 ($500)18 11/08/02 $175 12 11/15/02 $625 12 11/22/02 $725 8
11/29/02 $1,038 5 12/06/02 $688 7 12/13/02 $438 7 12/20/02 $663 7
12/27/02 $1,000 5 01/03/03 $250 7 01/10/03 $125 9 01/17/03 $1,050 7
01/24/03 $1,738 5 01/31/03 ($1,413)17 02/07/03 $138 9 02/14/03 $1,663 10
02/21/03 $713 6 02/28/03 $313 10 03/07/03 ($1,100)16 03/14/03 $1,588 13
03/21/03 $3,025 6 03/28/03 ($1,263)12 04/04/03 $50 10 04/11/03 ($300)12
04/18/03 $1,850 5 04/25/03 $663 8 05/02/03 $1578 8 05/09/03 $(938)10
05/16/03 ($500)11 05/23/03$1,038 7 05/30/03 $900 5 06/06/03 $775 8
06/13/03 $925 7 06/20/03 $538 6 06/27/03 $25 9 07/03/03($1,950) 8
07/11/03 $588 6 07/18/03 $638 6 07/25/03 $288 10 08/01/03 $225 9
08/08/03 $138 10 08/15/03 $125 8 08/22/03($475) 10 08/29/03 $688 8
09/05/03 $225 5 09/12/03 $313 8 09/19/03 $575 5 09/26/03($125)10
10/03/03 $850 8 10/10/03($988) 9 10/17/03 $213 7 10/24/03 $13 5
10/31/03($175) 7 11/07/03($100) 4 11/14/03 $350 6 11/21/03($525) 9
11/28/03 $88 6 12/05/03($125) 6 12/12/03($125)10 12/19/03$1,013 6
12/26/03 $150 4 01/02/04 $250 6 01/09/04 $863 5    
Nth Order Fading Memory Polynomial System Performance
(Daily Bars)
System Tradable 1997 Out-Of-Sample
% Return on 3X 1997 Margin
 1998 Out-Of-Sample
% Return on 3X 1998 Margin		 1999 Out-Of-Sample
% Return on 3X 1999 Margin		 Notes
nth Order Fading Memory Polynomial System Yen Futures Daily Bars
160%
154%
50%
 This is the system used in the "The Yen Recursed" article in the S&C Dec 1998 issue.
nth Order Fading Memory Polynomial System US Bond Futures Daily Bars
124%
118%
43%
 Applied to Bond futures this system used 2nd, 3rd and 4th degree fading memory polynomials as it walked forward in time.



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