Independent Indicators: historical volatility

[Mark Johnson <janitor@xxxxxxxxxxxx>]

To construct an orthogonal set of basis vectors
that span the space of technical indicators,
I think it would be necessary to include the
indicator "Historical Volatility", widely
employed by equity options traders:

   Let Series C[j] be the set of Closing prices
   Let Series y[j] = ln(C[j+1]) - ln(C[j])
   Let ave_y = mean value of the y[] series over the past n bars
   Then HV[j] = sqrt( SUM(y - ave_y) / (n-1) )

Notice that HV is a function of Price RATIOS since it
deals with differences of logarithms of price.
[recall ln(a/b) = ln(a) - ln(b)].  This is unique;
almost all other indicators (e.g. TrueRange, Random
Walk Index, etc) use raw prices rather than price ratios.

Also notice that HV is *not* a function of the open
price or the high price or the low price; it only operates
upon closes.