There's more to volatility than volume - Santa Fe Institute

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FIG. 4: Cumulative distribution of absolute (log) returns P (|r| > x) under several different time clocks, plotted on double logarithmic scale. (a, top) The LSE stock AZN (b, middle) The NYSE stock Procter & Gamble (PG) in the 1/8 dollar tick size period. (c, bottom) PG when the tick size is a penny. The time clocks shown are real time (black circles), transaction time (red squares), and volume time (blue diamonds). For comparison we also show a normal distribution (dashed black line) with the same mean and variance as in transaction time. For AZN we also show volume time for the on-book market only (green triangles). The real time returns are 15 minutes in every case; transaction and volume time intervals are chosen to match this. For both LSE and NYSE2 both the transaction time and volume time distributions are almost identical to real time, even in the tails. For PG in the NYSE1 data set the deviations in the tail from real time are noticeable, but they are still well away from the normal distribution.
FIG. 5: Cumulative distribution of normalized absolute (log) returns P (|r| > x) averaged over all the stocks in each data set under several different time clocks, plotted on double logarithmic scale. (a, top) LSE, (b, middle) NYSE1, (c, bottom) NYSE2. The time clocks shown are real time (black circles), transaction time (red squares), and volume time (blue diamonds). For the LSE we also show volume time for the on-book market only (green triangles). For comparison we also show a normal distribution (dashed black line) with the same mean and variance as in transaction time.
Page 1 and 2: There’s more to volatility than v
Page 3 and 4: themselves. Plerou et al. divide th
Page 5 and 6: privately, there are no published q
Page 7 and 8: B. Volatility in transaction time T
Page 9 and 10: FIG. 3: An illustration of the rela
Page 11: the majority of variation in volati
Page 15 and 16: FIG. 6: Cumulative distribution of
Page 17 and 18: FIG. 7: Test of the theory of Gabai
Page 19 and 20: FIG. 8: Computation of Hurst expone
Page 21 and 22: volatility market a b d (×100) R 2
Page 23 and 24: of the work in Farmer et al. (2004)
Page 25: [17] A. R. Gallant, P. E. Rossi, an

There's more to volatility than volume - Santa Fe Institute

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