1986issue C071-12
Evaluating daily price and volume serial independence windows
A signed daily series can be read as three related evaluation questions: whether plus and minus counts stay balanced, whether consecutive signs cluster, and whether a signed change is associated with a later lag. Editorial interpretation: stop the usable horizon at the first sampling lag that returns inside a pre-stated independence cutoff.
- Editorial: treat a signed daily series as three related evaluation questions, then stop the usable horizon at the first sampling lag that returns inside a pre-stated independence cutoff.
- A trading window is the last lag whose chi-square values all stayed at or beyond the chosen 95 percent cutoff before a later lag fell inside it.
- A one-day-lag chi-square on 24,785 signed daily closes was 74.30, above the 3.841 cutoff, while the matching volume sign-balance statistic was 0.10 and treated as random.
- Dropping 2,574 Saturday sessions shortened the 95 percent non-random price window from 51 days to 34 days and left the serial-dependence window nearly unchanged at 173 days versus 176.
Chi-square, runs, and lag association tests
A chi-square test is a goodness-of-fit comparison of observed plus and minus counts, or of consecutive-sign pair counts, against explicit random frequencies at a stated confidence cutoff. A runs test evaluates whether ordered plus and minus changes cluster or persist rather than alternating as independent signs would. An autocorrelation test evaluates whether a signed change at one sampling point is statistically related to signed changes at a defined lag.
Sign balance at a one-day lag
The evaluation used daily industrial-average closes and exchange total volume from 2 January 1897 through 31 December 1985, converting each series into plus or minus changes at a chosen lag.
A one-day-lag chi-square goodness-of-fit test on 24,785 signed daily closes produced a statistic of 74.30, above the 3.841 cutoff used for 95 percent non-randomness. The matching one-day-lag volume sign-balance chi-square was 0.10, below the same 3.841 cutoff, so daily volume sign changes were treated as random. Non-randomness tests used one degree of freedom, with a 95 percent cutoff of 3.841.
Consecutive signs and serial dependence
Serial dependence is a four-compartment count of consecutive sign pairs used to test whether a change depends on the previous change. Consecutive-sign compartment chi-squares were 4792.83 for price and 753.36 for volume, both above the 14.067 serial-dependence cutoff. Serial-dependence tests used seven degrees of freedom, with a 95 percent cutoff of 14.067.
Editorial interpretation: that compartment count is the runs-style question about whether signs cluster or persist rather than alternate as independent signs would.
Lag sampling and later association
Lag sampling repeats the same signed-change tests on every k-th observation so the horizon of a departure can be measured.
Editorial interpretation: repeating the signed-change tests at successive lags is how the lag-to-lag association question becomes a measured horizon.
Where the trading window stops
A trading window was defined as the last lag whose chi-square values all stayed at or beyond the chosen 95 percent cutoff before a later lag fell inside it. A trading window is the longest consecutive lag at which the chosen independence statistics remain outside a pre-stated confidence cutoff.
Full-sample price and volume windows
On the full calendar sample, the 95 percent non-random price-sign window was 51 days and the serial-dependence window was 176 days. Daily volume sign changes stayed random across lags, while serial dependence supported a 2-day window on the full sample.
What Saturday sessions changed
Dropping 2,574 Saturday sessions shortened the 95 percent non-random price window from 51 days to 34 days and left the serial-dependence window nearly unchanged at 173 days versus 176. After Saturday sessions were removed, volume serial dependence supported a 6-day window.
All readings on this track · 15 readings
- 1986Constructing runs and persistence tests from labeled prices
- 1986Evaluating daily price and volume serial independence windows
- 1986Evaluating advance-decline plus-day runs against chance baselines
- 1986Weekly resamples as a diagnostic filter for statistical windows
- 1988Runs test as a critique of price-series memory
- 1989Evaluating weekday close direction with a counted baseline
- 1989Statistical windows for indicator time parameters
- 1992Channel-height ratios for equity trend evaluation
- 2001A runs test before volatility and expected-value sizing
- 2005Constructing runs-test z-scores for signed return persistence
- 2005Evaluating persistence with runs and autocorrelation
- 2005Weekday FX turning points and close run tests
- 2013Constructing a runs-test turn forecast
- 2017Star rating from slope and swing runs
- 2018Regime-dependent odds after directional price runs