recent developments in high frequency financial ... - Index of

Intraday stock prices, duration, and volume 257
Table 2 Distribution of prices, duration, and volume
Percentiles
10 20 30 40 50 60 70 80 90
IBM Price change −3 −1 0 0 0 0 1 1 3
Duration 1 2 3 4 5 6 7 10 14
Duration (sell) 2 2 3 4 5 6 7 10 14
Duration (buy) 1 2 3 4 5 6 7 10 14
Volume 1 2 4 5 7 10 14 23 48
Volume (sell) 1 2 4 5 7 10 13 22 45
Volume (buy) 1 2 4 5 7 10 15 24 50
GE Price change −1 −1 0 0 0 0 0 1 1
Duration 1 1 2 2 3 4 5 7 11
Duration (sell) 1 1 2 2 3 4 5 7 11
Duration (buy) 1 1 2 2 3 4 5 7 11
Volume 1 3 5 8 10 15 24 42 94
Volume (sell) 1 3 5 8 10 15 24 40 90
Volume (buy) 1 3 5 8 10 15 24 43 99
BA Price change −2 −1 0 0 0 0 0 1 2
Duration 1 2 3 4 5 7 10 15 25
Duration (sell) 1 2 3 4 5 7 10 15 25
Duration (buy) 1 2 3 4 5 7 10 15 25
Volume 1 2 2 3 5 7 10 13 24
Volume (sell) 1 2 2 3 5 6 10 12 23
Volume (buy) 1 2 2 4 5 7 10 13 25
MO Price change −2 −1 0 0 0 0 0 1 2
Duration 1 2 3 3 5 6 8 11 18
Duration (sell) 1 2 3 3 5 6 8 11 18
Duration (buy) 1 2 3 3 5 6 8 11 17
Volume 1 2 3 5 6 9 12 20 42
Volume (sell) 1 2 3 5 6 9 12 20 41
Volume (buy) 1 2 3 5 6 9 12 20 43
frequently traded of the four stocks. The distribution of price changes is mostly
symmetric. Table 2 also provides a useful reference for interpreting our conditional
distribution plots, as our conditional probabilities will be estimated and plotted at
various percentile values of the conditioning information set.
3 Nonparametric estimation of conditional distribution functions
Let {X t,Y t} T t=1 be observations from a strictly stationary process where Y t is a scalar
and X t =(x 1t, x 2t,...x Mt). In our first application, Y t=Δp t and X t=(d t, sv t). One nonparametric
approach to estimating the conditional distribution function
Fyx ð j Þ ¼ PrðYtyjXt¼xÞ