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Working Papers

The Least Squares Velocity System

The Best Fit Straight Line. Let us imagine a set of closing prices on a graph with time as the horizontal axis and price as the vertical axis. Let us further suppose that we have only twenty closing price dots at twenty time intervals. How can we draw a straight line through those twenty prices such that the sum of all the squared differences between the prices at each time interval and the straight line that is being fit to the data is minimized? This is called the "Least Squares Fit" line of the data (also referred to as the linear regression line and Best Fit Line). This mathematical technique is available in most of today's technical analysis software.

The formula for the straight line is:

a + b*t

where a is the initial value of the line, b is the slope of the line, and t is the time of the bar. The slope b is also called the velocity. Velocity is defined as the change of position per unit time. Using the Best Fit Line formula above velocity would be:

Velocity = [a+b*(t+1)] - [a+b*t] = b

The velocity of the least squares straight line is used to create a system. The least squares velocity has the advantage that it is a natural random price noise inhibitor. We can create a system such that unless the velocity is greater than some threshold we will not buy or sell. A large percentage of price noise generates a lot of back and forth movements of small magnitudes. With a lot of systems this back and forth movement creates many false buy and sell signals. However using the least squares velocity we can filter many of the small price noise movements by requiring that the velocity be greater than some threshold before we act.

The Least Squares Velocity System Input Parameters

  • Len = The Least Squares lookback period.
  • vup = The velocity has to be greater than vup to generate a buy signal.
  • vdn = The velocity has to be less than -vdn to generate a sell signal.
  • XOpn = Used only for Intraday bars. Prevents buys or sells until XOpn bars have past since the open. 0 = Ignore. Note, this input parameter avoids many opening gap whipsaws.
  • Xtime, = Used only for Intraday bars. Exit position before or at the close. If XTime= 1610 then exit at 4:10pm EST. 0 = ignore .

My working paper on the The nth Order Polynomial Velocity System on E-Mini 1min Bars can be found on the papers Page

Product Description

The Least Squares Velocity system is orientated to short term trading in all bar ranges (1 tic, 1 min, 5min, etc., daily) and with any tradeable price series. This system can also be used on futures, stocks, options, and mutual fund data.

For TradeStation, Multicharts all of the EasyLanguage™ strategy and indicator codes are directly importable into your choice of TS9 or MC 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 strategy 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 intraday or daily futures the system was tested on, the user can easily use this system on any tradeable or on any time frame.

For NeuroShell Trader/DayTrader Pro, the Trading Strategy and Indicators are directly imported into NeuroShell via a special setup exe file and are fully disclosed in the Indicator wizard "MA_KeyTrSys" category and in the Trading Strategy Wizard "MA_KeyTrSys" directory. The C++ DLL code is not disclosed. The Input parameters to the strategy 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 intraday or daily futures the system was tested on, the user can easily use this system on any tradeable or on any time frame.

The accompanying page manual consists of:

  • A short tutorial on the details of performing walk forward optimization with out-of-sample testing using TradeStation and how I look for the "best" parameters in a TS combinatorial optimization run(available in the TS Manual only).
  • A complete description of the Least Squares Velocity system, it's derivation and it's input parameters.
  • The walk forward optimization method used and a table of the walk forward results for the system.
  • The input parameter test ranges
  • A chart printout with the Strategy and it's associated Indicator with all the system buy and sell signals displayed on the chart.
  • Performance Summaries for the test period and the out-of sample period segments.

In addition The Least Squares Velocity system has its exact duplicate in indicator form which is displayable on the price chart, so that the user can visually see how the buy and sell signals occur.

For TradeStation, MultiCharts The Least Squares Velocity System™ is one of the 9 systems included in the  Key Daily &Intraday Trading Systems package. The Key Daily &Intraday Trading Systems package is being offered through Meyers Analytics L.L.C. for $395. Shipping via Email consists of a zip file containing the Manual in Adobe PDF format, ELD file and DLL file.

For NeuroShell Trader/DayTrader Pro, The Least Squares Velocity System™ is one of the 6 systems included in the  Key Daily &Intraday Trading Systems package.. The Key Daily &Intraday Trading Systems package is being offered through Meyers Analytics L.L.C. for $395 . Shipping via Email consists of a zip file containing the Manual in Adobe PDF format and the MA-KeyTrSysSetup.exe setup file.

How To Order
To order online click Order Online. If you would like to talk to me about the product, please call me at (305) 549-5843 M-F 12pm to 5pm CST. All E-mail queries can be sent to support@meyersanalytics.com.

Thank you for your Interest....Dennis Meyers


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