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Trading based on price data 12,000 bars ago ?
> -----Original Message-----
> From: Bob Fulks [mailto:bfulks@xxxxxxxxxxxx]
> Sent: Saturday, March 18, 2000 10:41 AM
> To: Canyon678@xxxxxxx
> Cc: omega-list@xxxxxxxxxx
> Subject: Re: Warning about accuracy of Array functions in TS2000i
>
>
> At 1:39 AM -0500 3/18/00, Canyon678@xxxxxxx wrote:
>
> >Can you please elaborate, the difference between the two i.e
> current bar & the mod function
>
>
> They initialize the function by doing the detailed, complete
> calculation at CurrentBar = 1.
>
> They then calculate just the differences of the value for the new
> bar from that of the previous bar (by adding the value for the
> new bar and subtracting the one for the old bar that dropped off
> of the average).
>
> This saves a lot of calculations and is generally a good thing to
> do. But with only 16 bit arithmetic, the small errors of all the
> additions and subtractions can accumulate when you are talking
> about tens of thousands of bars.
>
> But simply replacing:
>
> if CurrentBar = 1 then begin
>
> with:
>
> if Mod(CurrentBar, 100) = 1 then begin
>
> would force the complete accurate calculation of the Average
> every 100 bars so the calculation would be accurate at every
> 100th bar. Then they would use the addition/subtraction scheme
> for the next 99 bars as in the original code. The errors would
> then only build up over 99 bars and would not be significant.
>
> The cost would be a complete calculation once out of every 100
> bars which would be insignificant.
>
> The "Mod" function returns the value of the remainder after
> dividing CurrentBar by 100 so the condition would be true on
> CurrentBar = 1, 101, 201, 301, ...
>
> To test it try the code listed below. On 12000 bars of INDU data
> I could see errors exceeding 0.03. It varies with the Length so
> try various values.
>
> The effect is small in this case but is often much larger in
> other cases, particularly those that multiply prices together or
> multiply prices by a length.
>
> A good example is the LinearRegressionSlope function. I applied
> it to 100 bars of INDU data (the DJIA) and had it print the
> values of all internal variables. The numbers were as follows.
>
> SumBars 4,950
> SumSqrBars 328,350
> SumY 1,103,023
> Sum1 54,584,252
> Sum2 5,459,962,368
> Len*Sum1 5,458,425,200
> Num1 -1,537,168 = 5,458,425,200 - 5,459,962,368
> Num2 -8,332,500
> SumBars*SumBars 24,502,500
> Len*SumSqrBars 32,835,000
>
> These are floating point variables so the accuracy might be OK
> for this application. But you can see how the numbers can get way
> out of the normal ranges we think about.
>
> Bob Fulks
>
> ----------------------------------------
>
> {Test Code for Average Function}
>
> Input: Length(4);
>
> Vars: Price(Close), EMax(0), EMin(0), Err(0), Ave1(Close), Ave2(Close);
>
> Ave1 = Average(Close, Length);
> Price = Close;
> Ave2 = Average(Price, Length);
> Err = Ave2 - Ave1;
>
> if CurrentBar > 100 then begin
> EMax = iff(Err > EMax, Err, EMax);
> EMin = iff(Err < EMin, Err, EMin);
> end;
>
> Plot1(Err, "1");
> Plot2(EMax, "2");
> Plot3(EMin, "3");
> Plot4(0, "4");
>
> ------
>
> This looks as if "Err" will always be zero but it will not be. Here's why:
>
> --------
>
> Ave1 = Average(Close, Length);
>
> This form will cause TradeStation to use the "series" version of
> the Average function, which is the one that has the problem we
> are discussing.
>
> --------
>
> Price = Close;
> Ave2 = Average(Price, Length);
>
> This code will cause TradeStation to use the "simple" version of
> the Average function which does an exact calculation on every
> bar. This is because we used a variable called "Price" as the
> input. (Look at the code for each function to see the difference.)
>
> --------
>
> Err = Ave2 - Ave1;
>
> This code finds the difference between the two versions.
>
> --------
>
> if CurrentBar > 100 then begin
> EMax = iff(Err > EMax, Err, EMax);
> EMin = iff(Err < EMin, Err, EMin);
> end;
>
> This code keeps track of the maximum and minimum error (after a
> start up period).
>
> -------
>
> Plot1(Err, "1");
> Plot2(EMax, "2");
> Plot3(EMin, "3");
> Plot4(0, "4");
>
> This code plots everything.
>
> ------
>
>
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