More on Waiting Times, from Vic Niederhoffer
It is interesting to contemplate the distribution of waiting times to the next 10 day max's and 10 day min's in S&P futures since 1 1 1999.
[Ed.: an n day max is defined by {for 1 = 1 to n, c[t] > c[t-i] } i.e. the close is higher than the previous n closes]
Col A: days since last 10 day minimum
Col B: Number of occurrences
Col C: Waiting time to next one
Col D: days since last 10 day maximum
Col E: Number of occurrences
Col F: Waiting time to next one
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
Col A Col B Col C Col D Col E Col F
0 524 0 789
1 297 10.5 1 373 8
2 219 13 2 276 9
3 188 14 3 226 10
4 165 15 4 185 11
5 146 15 5 161 11
6 140 15 6 148 11
7 130 15 7 131 11
8 124 15 8 119 11.5
9 119 14 9 115 11
10 110 14 10 108 11
11-15 426 15 11-15 375 11
16-20 289 15 16-20 226 12
21-30 339 16 21-30 257 11
31-50 288 13 31-50 257 11
51-100 54 06 51-100 11 05
There were 3575 trading days during this period with no drift per day, i.e. the adjusted futures started and ended at the same level.
Many assymmetries are evident.
The maxima occur with much greater frequency. The average waiting time to the next 10 day min or 10 day max is constant until 51 days has elapsed. The waiting time to the next 10 day minima is greater than the wait to the next day maxima after more than 10 days have elapsed.
I studied this because I am brushing up on my knowledge of stochastic models, reading many good books on the subject. I find the subject very refreshing and useful and it is good to keep the paper and pencil less feeble at counting.
One would point out that Mr. Tom Downing did very good work on writing this statistics program while he was employed by my firm. Vic, chair.