In the Least Squares Velocity System we examined a trading system that used the velocity of prices fit by a straight line, through “N” past prices, to determined buy and sell points. The reasoning behind this type of system was to only trade when the price trend velocity was above a certain threshold. Many times prices are meandering around without a notable trend. At these times we do not wish to trade because of the whipsaws losses that occur from this type of price action. When a price trend finally starts, the velocity of that price trend moves above some minimum value. Thus the velocity system would only issue a trade when certain velocity barriers were crossed. Acceleration is the change in velocity per unit time. In order for velocity to reach a certain value the price changes must start accelerating. Thus acceleration should be an even earlier indicator than velocity that prices are starting to trend. Unfortunately to find acceleration we cannot use the straight line formula. Straight lines have only constant velocities and no acceleration. We have to use a 2nd order polynomial to fit N past prices in order to find the price acceleration.
The formula for the 2nd
order polynomial is:
p(t)est = a + b*t +c*t2
is the estimated price found from the least squares fit at time t. a, b and c
are the coefficients that are determined by the least squares fit of the 2nd order polynomial to N past prices. Using the formula above acceleration would be the second derivative of p(t)est
and would be 2c
The acceleration component of a least squares 2nd
order polynomial fit to N past prices is used to create a system. The least squares acceleration has the advantage that it is a natural random price noise inhibitor. We can create a system such that unless the acceleration 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 acceleration we can filter many of the small price noise movements by requiring that the acceleration be greater than some threshold before we act. A super fast algorithm for computing the least squares acceleration at each price bar is used that cuts the computation time by 80% and avoids floating point overflow.
The Least Squares Acceleration System Input Parameters
- N = The number of prices used in the calculation of the Least Squares acceleration.
- aup = The acceleration has to be greater than the threshold aup to generate a buy signal.
- adn = The acceleration has to be less than the threshold -adn 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 Acceleration System
can be found on the Papers Page
The Acceleration 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 Acceleration 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 Acceleration 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 Acceleration System™ is one of the 9 systems included in the 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 Acceleration System™
is one of the 9 systems included in the . The Key Daily &Intraday Trading Systems package is being offered through Meyers Analytics L.L.C.
. 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
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. 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 email@example.com.
Thank you for your Interest....Dennis Meyers