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Gary, extending your thoughts, have you found similar correlations in other
markets? Naz vs. ND M1? CIEN daily vs. 10 min. intraday? ND M1 daily vs. 10
min.?
TIA
Gene
----- Original Message -----
From: "Gary Fritz" <fritz@xxxxxxxx>
To: "Omegalist" <omega-list@xxxxxxxxxx>
Sent: Saturday, May 19, 2001 10:55 AM
Subject: Re: trendiness measures
> > Could someone please briefly explain some measures of trendiness
> > that I could use to decide which markets tend to trend more than
> > others? ... Yes, I'm familiar with the ADX, the CMO, etc., but
> > how are indicators like these used to give a summary of a market's
> > trendiness over, say, a year?
>
> Here's an indicator you can apply to a market to get a statistical
> measure for its trendiness. It measures the movement of the market
> over several sample lengths, and compares the result to what would be
> expected of a "random walk." If the market has moved more than a
> random walk, that indicates it tends to trend in that timeframe. If
> it moves less, it's *anti*-trending -- that is, it reverses more than
> would be expected of even a random walk.
>
> Also note that you must apply it to a chart with AT LEAST 100 bars.
> Longer charts will give you a more accurate result.
>
> Here's an example of the indicator's output:
>
> Trend data for SP M1:
> 10-minute bars
> 1926 samples
> Bars StdDev Expected Actual
> 1 0.00260 1 1.00000
> 4 0.00492 2 1.89514
> 9 0.00761 3 2.93162
> 16 0.01032 4 3.97341
> 25 0.01313 5 5.05649
> 36 0.01590 6 6.12256
> 49 0.01835 7 7.06543
> 64 0.02091 8 8.05145
> 81 0.02333 9 8.98652
> 100 0.02536 10 9.76810
>
> Since the "Actual" value for the sample lengths 25, 36, 49, and 64 is
> slightly longer than the "Expected," that indicates the 10min SP
> tends to trend (slightly) in this period when you look at 25-64 bar
> moves. Longer and shorter moves tend NOT to trend, since their
> "Actual" value is slightly LESS than the "Expected."
>
> Here's an interesting result: this is a year of DAILY S&P:
>
> Bars StdDev Expected Actual
> 1 0.01399 1 1.00000
> 4 0.02595 2 1.85540
> 9 0.03649 3 2.60854
> 16 0.04641 4 3.31798
> 25 0.05049 5 3.60985
> 36 0.05489 6 3.92427
> 49 0.05456 7 3.90075
> 64 0.05884 8 4.20646
> 81 0.06229 9 4.45316
> 100 0.06400 10 4.57589
>
> Note that the S&P shows anti-trending (reversing) behavior at ALL
> sample lengths, especially at longer lengths. This should come as no
> surprise. The S&P is known as a reversing market -- that's why "buy
> the dips" works. "Trending" means "if it's going up, it will tend to
> keep going up, and vice versa." But in the S&P it usually works to
> say "if it's going down, buy, because soon it will go back up."
> That's ANTI-trending behavior.
>
> By default the indicator DOES NOT PLOT ANYTHING. It prints its
> results in the Print Log. Several people had trouble with that the
> last time I posted an indicator like this. Remember to scroll down
> to the bottom of the Print Log. :-) If you set the PlotSD input to
> True, it will plot the SD's of several sample lengths, but I don't
> think this is very useful.
>
> Gary
>
>
>
{***************************************************************************
> *
> * Indicator: Trend StdDev
> * Gary Fritz 1/7/99
> * 7/20/99: Minor fixes and improvements
> *
> * Computes the standard deviation of Nlengs different lengths of
> * price action: C-C[1], C-C[4], C-C[9], C-C[16], etc.
> * In a pure Random Walk, the N^2-length sample will have a StdDev
> * of N times the StdDev of the 1-length sample. If a particular
> * price example shows larger-than-expected StdDevs it indicates
> * a trending market; if the StdDevs are smaller than the expected
> * values it indicates an anti-trending (reversing) market.
> *
> * Doesn't start recording data until 100 bars are available.
> * Needs a lot of bars to compute valid data anyway, so just apply it
> * to a long chart.
> *
> * StdDev values are printed to the Print Log.
> *
> * References:
> * TASC Aug 95, Alex Saitta, Trending on a Historical Basis
> * TASC Jan 92, E. Michael Poulos, Futures According to Trend Tendency
> * (Thanks to Dave Chamness for the pointer & explanation!)
> *
> * Inputs: Price Price point used in SD calculations
> * PlotStD If true, plots StdDev for 4 sample lengths
> * (Probably not very useful)
> *
>
***************************************************************************}
>
> Inputs: Price(Close),
> PlotStD(False); { Plot Std Devs of 9, 25, 49, 81-long
samples }
>
> Vars: Nlengs(10); { Compute stddev for lengths 1:Nlengs^2 }
> Vars: Nbars(0), Index(0), Barsback(0), Diff(0), Mean(0), Sigma(0),
SD1(0);
> Arrays: BarSum[20](0), BarSum2[20](0);
>
> if (currentBar = 1) then begin
> for Index = 1 to Nlengs begin
> Nbars = 0;
> BarSum[Index] = 0;
> BarSum2[Index] = 0;
> end;
> end;
>
> { On each bar, add up sums & sum-of-squares,
> for lookback lengths of Index^2 }
>
> if (currentBar > Nlengs*Nlengs) then begin
> Nbars = Nbars+1;
> for Index = 1 to Nlengs begin
> if Price[Index*Index] = 0
> then Diff = 0
> else Diff = (Price - Price[Index*Index]) / Price[Index*Index];
> BarSum[Index] = BarSum[Index] + Diff;
> BarSum2[Index] = BarSum2[Index] + Diff*Diff;
> end;
> end;
>
> if LastBarOnChart and (Nbars > 1) then begin
> print("Trend data for ",GetSymbolName,":");
> if (DataCompression = 4) then print(" Monthly bars")
> else if (DataCompression = 3) then print(" Weekly bars")
> else if (DataCompression = 2) then print(" Daily bars")
> else if (DataCompression = 1) then print(" ",BarInterval:3:0,"-minute
bars");
> print(Nbars:5:0," samples");
>
> { An N^2 day test, with a perfect random walk, is expected to have
> a standard deviation N times larger than a 1-day test.
> So the "Expected" column is N, and the "Actual" column is
> N^2-day_StdDev / 1-day_StdDev. }
>
> print("Bars StdDev Expected Actual");
> for Index = 1 to Nlengs begin
> Mean = BarSum[Index] / Nbars;
> Sigma = SquareRoot((BarSum2[Index]-Nbars*Mean*Mean)/(Nbars-1));
> if (Index = 1) then SD1 = Sigma;
> print(Index*Index:4:0," ",Sigma:2:5," ",Index:2:0,"
",Sigma/SD1:2:5);
> end;
> end;
>
> { If desired, plot 4 of the SD's. I'm not sure this is useful but
> I thought somebody might like to see it. The repeated code is not
> very pretty, but EL's limits made it a pain to do it via looping. }
>
> if PlotStD and (Nbars > 10) then begin
> Mean = BarSum[3] / Nbars;
> Sigma = SquareRoot((BarSum2[3]-Nbars*Mean*Mean)/(Nbars-1));
> plot1(Sigma, "StD3");
> Mean = BarSum[5] / Nbars;
> Sigma = SquareRoot((BarSum2[5]-Nbars*Mean*Mean)/(Nbars-1));
> plot2(Sigma, "StD5");
> Mean = BarSum[7] / Nbars;
> Sigma = SquareRoot((BarSum2[7]-Nbars*Mean*Mean)/(Nbars-1));
> plot3(Sigma, "StD7");
> Mean = BarSum[9] / Nbars;
> Sigma = SquareRoot((BarSum2[9]-Nbars*Mean*Mean)/(Nbars-1));
> plot4(Sigma, "StD9");
> end;
>
>
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