Morning Brief: WTI at $99.87 as ISM Opens the Payrolls Week

A timing-date study often begins with an average return around a predeclared window. MacKinlay describes another question: what fraction of abnormal returns have a positive sign? His sign test considers positive versus negative outcomes rather than letting a single large magnitude dominate the tally. Under its stated null, the expected positive fraction is one half, and returns are independent across securities. Those are assumptions to test, not properties of an arbitrary group of charts. For an editorial Gann-date example, suppose ten separately selected event observations yield seven positive abnormal returns. The observed fraction is 0.70. Relative to a one-half null, MacKinlay's asymptotic statistic is (0.70 − 0.50) times the square root of 10, divided by 0.50, or approximately 1.265. That calculation describes the toy count; it does not establish a timing effect or a reliable probability from only ten cases. Compare it with the mean abnormal return under the same date rule. If the mean is positive but the sign tally is mostly negative, identify the outliers instead of declaring broad confirmation. Keep the selection window, benchmark and eligible observations fixed before counting.

Try it

In a synthetic sample of 10 independent event observations, seven abnormal returns are positive. Calculate the positive fraction and the illustrative sign statistic (p̂ − 0.5)√N/0.5. What would the statistic be for eight positives?

Limits

MacKinlay warns that the sign test assumes independent observations and a one-half positive base rate. Skewed daily abnormal returns can undermine its specification. Shared dates and correlated assets can violate independence; this example is not a market forecast.

Source

A. Craig MacKinlay, Event Studies in Economics and Finance, Journal of Economic Literature 35(1), 1997, printed p. 32, Section 8, Nonparametric Tests, equation (23). Peer-reviewed finance methods paper reproduced as a searchable public court exhibit; example counts are editorial, not observations from its 1989–1993 earnings sample.

Today

Latest completed UTC daily session: 2026-11-01 (closed 2026-11-02 00:00 UTC); BTC closed $78,230.55 and ETH $2,272.23. Across the ten daily close-to-close BTC-minus-ETH percentage-return differences dated 2026-10-23 through 2026-11-01 (base closes 2026-10-22), 6/10 were positive (fraction 0.60), giving an illustrative sign statistic of 0.632456. For the full brief, plot the 11 BTC and ETH closes on the same UTC-dated chart using separate USD axes or both indexed to 2026-10-22 = 100; add each daily spread sign on its matching 2026-10-23 through 2026-11-01 date, not on the next morning. This is a correlated crypto proxy sample, not ten independent predeclared Gann events or abnormal returns. Neither independence nor a half-positive null is established; the statistic is descriptive, not evidence of a timing edge. Coinbase Exchange BTC-USD daily percentage return minus ETH-USD daily percentage return, Latest session 2026-11-02T00:00:00+00:00: ((positive_count/n_observations - 0.5)*sqrt(n_observations)/0.5) = 0.6324555320336758 dimensionless illustrative sign statistic (inputs: latest_btc_close_usd=78230.55, latest_btc_return_pct=1.0417573470131605, latest_eth_close_usd=2272.23, latest_eth_return_pct=0.8687507213694032, latest_spread_percentage_points=0.17300662564375724, n_observations=10, null_positive_fraction=0.5, positive_count=6, positive_fraction=0.6). Data source 1 Data source 2

A planetary station is often drawn as a dot where its zodiac longitude stops changing. But a one-dimensional pause is not a full stop in the sky. JPL Horizons separates observer-centered apparent ecliptic longitude and latitude (quantity 31) from total apparent plane-of-sky angular motion (quantity 47). The latter has a magnitude in arcseconds per minute and a position angle; longitude and latitude are in degrees. To classify a candidate station, take the same planet at two UTC timestamps a day apart. Compute the shortest signed change in longitude, with wraparound at 360 degrees. A near-zero change says only that the longitude component is small over that interval. Compare the latitude readings and Horizons' total sky-motion rate at the later timestamp. If latitude changes or sky motion is nonzero, the planet remains in apparent motion. A stationary longitude can coexist with a moving image. This distinction matters when a chart calls an exact station a timing mark. Declare the coordinate, observer, threshold, sampling interval, and ephemeris before looking at price. Do not replace longitude motion with total motion midway through an audit: they answer different questions. Even a valid station timestamp is only a time marker for subsequent market measurement, not a directional price signal.

Try it

Hypothetical Earth-centered apparent ecliptic readings, one UTC day apart: longitude 210.00° then 210.00°, latitude +1.00° then +1.20°. Compute the sampled longitude change, latitude change, and approximate latitude-only angular speed in arcseconds per minute. Is the image motionless?

Limits

A one-day difference can miss a reversal within the day; refine samples before estimating an instant. JPL’s instantaneous plane-of-sky rate is not identical to a finite-difference ecliptic rate. Apparent positions depend on observer and ephemeris. Coincidence with a BTC return does not establish cause, price direction, or an edge.

Source

JPL Horizons Manual, Observer Table, quantities 31 (observer ecliptic longitude and latitude) and 47 (sky motion: angular rate, direction position angle, and path angle). Primary NASA/JPL Solar System Dynamics documentation. The example readings are hypothetical, not observations.

Today

Mars apparent ecliptic longitude advanced 0.5020344 degrees from 2026-11-01T00:00:00Z to 2026-11-02T00:00:00Z, above the predeclared 0.05 degrees/day near-flat threshold: this is not a sampled longitude station. Latitude rose 0.0209749 degrees, while the separate instantaneous plane-of-sky motion at 2026-11-02T00:00:00Z was 1.2512741 arcseconds/minute. BTC-USD's completed 2026-11-01 UTC daily close was $78230.55, versus $77423.98 for 2026-10-31, a 1.04175735% close-to-close return. These simultaneous observations do not show direction or causality from Mars. Mars, geocentric apparent ecliptic coordinates; Coinbase Exchange BTC-USD daily closes, Latest session 2026-11-02T00:00:00Z: ((later_obs_ec_lon_deg - earlier_obs_ec_lon_deg + 180) % 360) - 180 = 0.5020344 degrees/day (inputs: btc_2026_10_31_daily_close_usd=77423.98, btc_2026_11_01_daily_close_usd=78230.55, earlier_obs_ec_lat_deg=1.6004264, earlier_obs_ec_lon_deg=138.6216809, earlier_sky_motion_arcsec_per_min=1.2594403, later_obs_ec_lat_deg=1.6214013, later_obs_ec_lon_deg=139.1237153, later_sky_motion_arcsec_per_min=1.2512741, near_flat_longitude_threshold_deg_per_day=0.05). Data source 1 Data source 2