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Some Numerical Queries, by Victor Niederhoffer

The recent S&P moves relative to open, high, and low cry out for description and prediction.

S&P Futs    Day   Open    High    Low     Close
20-Oct-06   Fri   1374.5  1375.5  1369.8  1374.9
23-Oct-06   Mon   1371.6  1384.2  1370.1  1380.7
24-Oct-06   Tue   1379.0  1385.3  1378.2  1384.8
25-Oct-06   Wed   1383.0  1389.5  1381.4  1389.2
26-Oct-06   Thr   1392.0  1395.2  1385.0  1392.9
27-Oct-06   Fri   1391.0  1392.2  1381.2  1384.8
30-Oct-06   Mon   1381.3  1386.8  1378.9  1383.2
31-Oct-06   Tue   1385.3  1387.1  1377.1  1383.2
01-Nov-06   Wed   1386.1  1386.9  1370.9  1372.9
02-Nov-06   Thr   1368.8  1373.5  1367.3  1371.3
03-Nov-06   Fri   1375.8  1377.2  1365.6  1368.5
06-Nov-06   Mon   1372.8  1386.3  1372.6  1383.8
07-Nov-06   Tue   1385.0  1391.7  1383.3  1391.0
  1. A run of six lower lows in a row was broken on Monday.
  2. A run of six days without a rise was broken.
  3. The high on Monday was below but within 1 point of three highs of the previous week.
  4. The change at the open on Monday was within a quarter point of the change on the previous day.
  5. Two up opens in a row more than four occurred in conjunction.
  6. Hopes were dashed on Friday when a nice up open was followed by a move down of 12 points.
  7. Wednesday of the previous week the high-low range was 16 points and Friday the high-low range was 12 points but the other three days the range was below 10.
  8. A string of six weeks up in a row was broken last Friday with a down week, giving the bears hope.
  9. The volume on Tuesday end of month was 50% higher than the average for the other days in conjunction with an unchanged day.
  10. The low on Monday was just a quarter point below the open and the high last Friday was just 1 point below the open. Similar low maximum within day moves above open occurred on 10/27, 10/31, and 11/03.

Many queries as to randomness, predictability, and further observations and hypotheses arise.