Well, your short mathematical examples are surely accurate, but it seems to me that the examples are far from practical trading reality using moving averages etc. For example, what reasonable prices move from 1 to 5, or from 1 to 100 in 5 bars, quotes, or trades, or in 5 steps? And especially where moving indicator values are used (EMA, SMA, etc), the example values would still produce clear changes in output values with each new value. So I'm not sure what the examples are intended to illustrate.
You also say that "the median is much more likely to be unaffected by outliers, spurious/bad data etc", but to be precise, the median will of course be 100% affected by outliers and bad data, exactly in proportion to the median and indicator mathematics calculations, no more and no less.
My main claim is only that the values of essentially all practical indicators will vary with changes in price inputs, regardless of what combination of BarData values are used. Some combinations (eg median, weighted, etc) may cause the indicator values to change a little less, some a little more.
Isn't that the way it should be?the mathematics of an indicator should force a change in the indicator output values when the input values changeelse what good would a constant indicator be?
I could be wrong, but it seems to me that the only real question about any indicator is whether or not its input and indicator mathematics have the combined characteristics that you want for your strategies.
I suppose that's part of the strategy gameto find or make indicators that have the change (indicator) characteristics that you want for your strategies. And of course no one but you can say whether a particular set of indicator mathematics for inputs (close, median, weighted, etc) and outputs (change in indicator value) is satisfactory for your strategy.
