Trading is about risk estimation that is to say probability of extremes. Today statisticians working in financial field try now to focus on extremes studies instead of mean studies using for example fractal models like Mandelbrott see his article: "A Multifractal Walk Down Wall Street"
http://www.elliottwave.com/education/SciAmerican/Mandelbrot_Article2.htm
"These techniques do not come closer to forecasting a price drop or rise on a specific day on the basis of past records. But they provide estimates of the probability of what the market might do and allow one to prepare for inevitable sea changes. The new modeling techniques are designed to cast a light of order into the seemingly impenetrable thicket of the financial markets. They also recognize the marinerâs warning that, as recent events demonstrate, deserves to be heeded: On even the calmest sea, a gale may be just over the horizon."
Further more a trend is defined by higher high or lower low by traditional technical analysts and my model confirms their point of view although before I discovered this model I thought it was rather ridiculous because probability law of highs and lows is highly unstable and normally difficult to estimate (that's why mandelbrott and other researchers work on this subject
) compared to the probability law of the mean ... but this suppose as premisce for this logical statement that the underlying law is truly stochastic and it is not the case finally my model shows that the law is or at least has a predominant deterministic law component hidden inside the stochastic apparent noise. More generally many things can be discovered by looking at the implicit premisces. People generally focus on the explicit conclusion they rarely care about the premisces so the inevitable errors when they apply the conclusion whereas the premisce is not true.
The practical usefulness of high and low of the day is for example the famous ATR entering into volatility estimation for breakout system. Why use ATR instead of standard deviation ? Because standard deviation is underestimating volatility if people usually determine statistical zone with a coefficient of 2 standard deviations thinking that it will encompass 95% of all points. This is roughly true for mean of a sample but as said above about risk we are less interested by mean than by extremes in trading. So ATR is not used practically only because it is simpler to calculate than standard deviation although this could be the justification in the past when computers had high cost
http://www.elliottwave.com/education/SciAmerican/Mandelbrot_Article2.htm
"These techniques do not come closer to forecasting a price drop or rise on a specific day on the basis of past records. But they provide estimates of the probability of what the market might do and allow one to prepare for inevitable sea changes. The new modeling techniques are designed to cast a light of order into the seemingly impenetrable thicket of the financial markets. They also recognize the marinerâs warning that, as recent events demonstrate, deserves to be heeded: On even the calmest sea, a gale may be just over the horizon."
Further more a trend is defined by higher high or lower low by traditional technical analysts and my model confirms their point of view although before I discovered this model I thought it was rather ridiculous because probability law of highs and lows is highly unstable and normally difficult to estimate (that's why mandelbrott and other researchers work on this subject
) compared to the probability law of the mean ... but this suppose as premisce for this logical statement that the underlying law is truly stochastic and it is not the case finally my model shows that the law is or at least has a predominant deterministic law component hidden inside the stochastic apparent noise. More generally many things can be discovered by looking at the implicit premisces. People generally focus on the explicit conclusion they rarely care about the premisces so the inevitable errors when they apply the conclusion whereas the premisce is not true.The practical usefulness of high and low of the day is for example the famous ATR entering into volatility estimation for breakout system. Why use ATR instead of standard deviation ? Because standard deviation is underestimating volatility if people usually determine statistical zone with a coefficient of 2 standard deviations thinking that it will encompass 95% of all points. This is roughly true for mean of a sample but as said above about risk we are less interested by mean than by extremes in trading. So ATR is not used practically only because it is simpler to calculate than standard deviation although this could be the justification in the past when computers had high cost

Quote from stock777:
Isn't it archaic and ridiculous to calculate the index based on EXTREMES for the day? Sounds like a throwback to the days when grey men wearing eyeshades had to do the math.
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