Quantifying randomness: variance ratio

Discussion in 'Strategy Building' started by stephencrowley, Feb 14, 2006.

  1. squeeze

    squeeze

    Have you managed to extend it to trend analysis using intra-day interval data?

    This will be different from a daily trend analysis due to the over-night intervals and the intra-day volatility structure.
     
    #41     Feb 16, 2006
  2. I trade exclusively intraday.. overnight returns are problematic due to the low sample size.. would be nice if the markets traded 24/7...but even then there would be seasonal activity.

    The intraday trend analysis probably has no relation to daily trend analysis.. but that is just a guess, I don't have any daily data to test...

    No extension of the VR is necessary.. just prepare your data properly.

     
    #42     Feb 16, 2006
  3. squeeze

    squeeze

    The concept should be extendable to trend analysis over the active trading session.

    For the daily version I modified the variance calculation (ln(C/C[n]))^2 which is correct for log normally distributed returns.

    The calculation in the paper is a close approximation.
     
    #43     Feb 16, 2006
  4. What do you mean by "daily version"? The calculation is the same no matter what your frequency of choice is.

     
    #44     Feb 16, 2006
  5. So do you guys think this 1.67 number can be extended intraday? For example a 10 min chart would have its own HV right. Can you take the open to close 10 min bars for the past 30 10M periods lets say and run this test and decide that anything > 1.67 shows mean reversion so fade the spikes vs. the 10M bars that show < 1.67 which implies , at the least, don't fade the spikes? THanks
    I can't see using the daily data as a judge on how to approach intra-day trading. Woudn't that be disastrous?
     
    #45     Feb 16, 2006
  6. To be clear, the variance ratio doesnt depend on any magic numbers and doesnt use highs, lows, etc and can be used on any time frame. I cant speak for these other measures.

     
    #46     Feb 16, 2006
  7. squeeze

    squeeze

    If the calculation in the paper is applied to intra-day data without modification I would expect the results to be skewed by the over-night volatility. Markets with high over-night volatility would appear more trending as a result.
     
    #47     Feb 16, 2006
  8. I see what you are saying.. that is only true if you were to concatenate intra-day returns together and ignore overnight changes.. this is not a good idea.

    Basically, I calculate a variance ratio profile for each day using intraday data.. and then overlay them.. if they are all very similiar then they are "consistently random" across the days analyzed.

    However, I've found some symbols that are trending many days and then pure random walks on others. I guess it basically quantifies what traders call intuitively "choppy" and "trendy" markets.

     
    #48     Feb 16, 2006
  9. squeeze

    squeeze

    I can see how you could calculate a single variance ratio number for each day but how do you calculate a variance ratio profile?
     
    #49     Feb 16, 2006
  10. Since the defintion of the variance ratio (or modified variance ratio) is the relative difference between 1-period changes vs N-period changes then you just calculate all the variance ratios from 1 to M and plot them.

    Note: you must use overlapping returns when calculating the N-period differences

    e.g.

    [sum(1:3) sum(2:4) sum(3:5)] etc


    vr(1,1) is always = to 1 by definition

    vrProfile=[var(1,1) var(1,2) var(1,3) ...var(1,M)];

    You can also fit a polynomial to the VR profile and it'll define 99% of the profile with only the first two coeffecients.

     
    #50     Feb 16, 2006