Showing posts with label AP Index. Show all posts
Showing posts with label AP Index. Show all posts

Monday, September 7, 2026

Physics-Based Forecasts of Investment Sentiment | Jeffrey A. Hansen

Hansen's February 2026 paper Physics-Based Forecasts of Investment Sentiment proposes that shifts in investor optimism and pessimism correlate with heliocentric planetary orbital geometry, sunspot activity, and Schumann resonance stability, rather than solely with economic news. The clock of investor sentiment is a roughly 90° Sun–vertex angle (86°–94°) between the Mercury–Saturn center, weighted by tidal force (T ∝ m/r³), and the Jupiter–Neptune center, with weights fitted in December 2000 to Hansen's Market Resilience Index (MRI). Clusters of these configurations define Anxiety-Free Periods (AFPs)—multi-month stretches of investor optimism—that typically fade when the final 90° column expires (plotted orange in charts below).
 
Geometry of the Inner Orbital Center (Mercury, Venus, Earth, Mars, Jupiter, Saturn) and the Outer Orbital Center (Jupiter, Saturn, Uranus, Neptune; Jupiter and Saturn sit in both centers): two mass-weighted planetary-group centers with the Sun at the vertex. When the angle is near 90° (Hansen uses 86°–94°), an AFP column is active, plotted as orange bars/columns in the US Stock Market Price Level chart below.
Physics Times the Turn; Economics Sizes the Move
Across thirteen AFPs from 1933–2024, the average cumulative gain is about 28%, followed by a 13% post-peak decline—near the 98th and 95th percentiles of duration-matched history. Physics is proposed to time the turn; economics to size it. 
 
Thirteen AFPs, named by the year of the price peak (1933-2024, exact dates in the chart above): geometry window = first 90° event through last 90° event; prior/post lows and returns are his market annotations (visually dated orange on the DJIA chart below). Average prior low is about 2½ months before the first event. The fourteenth cluster is the 2026 AFP (not in the 1933–2024 sample). Appendix U dates its 90° Fridays as Apr 24–May 22, 2026; Aug 07–Sep 18, 2026; and Nov 20–Dec 04, 2026. There is no completed peak/post-low for that episode yet.
US Stock Market Price Level (Log) vs. AFPs, 1920–2024.
A century of prices with orange AFP columns; column height represents intensity.
Each column is one 90° configuration event. A cluster of those bars is one Anxiety-Free Period.
2026 has three columns (late April–May, August–September, November–December).
 
Pre-peak ("boom") and post-peak ("bust") cumulative returns for the thirteen Anxiety-Free Periods since 1933, with empirical percentile ranks based on duration-matched periods in the full weekly Dow Jones Industrial Average history. The ranks measure the share of same-duration historical periods with less extreme returns. High percentiles show that gains consistently fall in the extreme tail, while declines do so in most cases. 
From Orbital Angles to Schumann Standing Waves to Human Physiological Entrainment
Market impact is attributed not to the angle itself, but to a four-step causal chain ending in Schumann-type modes, the Earth's ionospheric waveguide ringing at approximately 8, 14, and 21 Hz. A 90° configuration is hypothesized to laminarize solar emissions, stabilize ionospheric height, and lock global standing-wave frequencies near 14–21 Hz; this coherence is then linked to analytical optimism, with overlap in the 13–30 Hz EEG band.

Hypothesized causal mechanism for Anxiety-Free Periods. The diagram proposes a causal chain from solar-system geometry through solar emissions, ionospheric stability, global electromagnetic standing waves, and human physiological entrainment. It is repeated at the start of each section, highlighting the relevant step; here, Element 1 is highlighted.

Established Space-Weather Physics and Speculative Solar-Geometry Links
Stabilized solar output and ionospheric height extend accepted space-weather physics; the solar-geometry and cognition links remain speculative. Intensity scales with outer-group clustering, measured by Sun-to-outer-center distance, which is offered as the reason 1937 and 1987 were violent while 2006 was mild. Intensity is already represented by the column heights in the US Stock Market Price Level chart above.
 
Ap Index, F10.7, and Sunspots as Fellow Travelers
The same geometry used to time AFPs is associated with tighter co-movement among Ap Index, F10.7, sunspots, and Oulu neutron-monitor counts when the outer planets cluster. Geomagnetic and radio-flux series are treated as companions of standing-wave stability rather than as separate daily trading signals.

 Correlations of Solar Energy Metrics by High Intensity and Low Intensity Weeks.
Ap, F10.7, sunspots, and Oulu neutrons co-move more tightly when the outer group is clustered.

The Frozen Eight-Driver Orbital Model
An eight-driver orbital model—six frozen orbital-geometry factors covering planet-group angles, distances, and clusters, plus the predicted AFP and M-Spike series—was calibrated through late 2000 and then frozen. Using NASA coordinates alone, it forecasts the 14-week RSI from December 2000 through April 2024. Here, 14-week RSI means Wilder's Relative Strength Index calculated on weekly bars with a 14-week lookback: Hansen's proxy for multi-month price momentum and investor sentiment, rather than the more common 14-day RSI. The M-Spike is a short-term orbital-geometry factor—not an RSI or an AFP—computed from planet-group positions and read on DJIA/S&P prices as a multi-week M pattern: lift, mid-dip, rebound, and fade. About 88% of predicted turns match actual turns within ±1 week, versus a chance baseline near 0.25% (p < 0.001).

Predicted and Actual 14-week RSI for the US Stock Market, December 1, 2000–April 1, 2024.
Frozen-model path versus realized RSI and log price; the 88% out-of-sample test begins here.
 
When Price Rises but Sentiment Does Not
When actual RSI runs below the geometry path, as in 2007–08, Hansen interprets the divergence as economically driven pessimism despite rising prices. Pre- and post-event weekly returns around 26 individual 90° events differ less than 0.01% (p < 0.0001).
 
 Predicted and Actual 14-week RSI, Periods A and B. Arrow A marks the 2007–08
actual-RSI divergence below geometry; B marks an AFP in which both rise together.
 
The Limited Schumann-Resonance Test
Usable standing-wave data exist only from June 2015 through December 2021. However, it is not a published Schumann-resonance product. Hansen built the series himself from British Geological Survey magnetometer records at Eskdalemuir, Scotland. Within that window, the predicted 2017 AFP series is associated with frequency stability in modes 2–3 (p < 0.001), although is only about 0.05—the most direct test of standing-wave market impact, but also the thinnest.
 
US stock-market price and indicators for the 2017 Anxiety-Free Period and M-Spike episodes, June 05, 2015–December 31, 2021. The chart overlays market price, episode indicators, and ellipses A–D marking notable relationships between price patterns and episodic signals. It also shows modes 2 and 3 electromagnetic standing-wave stability, measured on weekends from 8 a.m. to 4 p.m. local time and lagged approximately two weeks. 
Sunspots as the Longer Proxy
Solar activity is more stable during 21 of 26 90° events and more often declines by day +21 after an event ends. Shorter geometry-defined M-Spikes (53 cases, 1940–2023) show weaker weekly-return significance (p ≈ 0.19).
 
Mega Cycle and Phase 1 Valuations
The same inner–outer angle maps onto a four-phase Mega Sentiment Cycle. Phase 1, from 0° to the AFP at 90°, has accounted for about 32% of weeks since 1942 but 53% of returns, with higher S&P 500 P/E ratios but no corresponding growth differential.
 
Mega Sentiment Cycle (2004–2027), showing its four phases, the timing of Anxiety-Free Periods, and the changing Inner Center–Sun–Outer Center angle. Stock Index Price refers to the DJIA, S&P 500, or related ETFs. 
How Panic Is Supposed to Spread
A Geoffrey Moore-style adoption model divides the market into Pioneers (~15%), Early Majority (~35%), Late Majority (~35%), and Laggards (~15%). Micro geometry is said to move the Pioneers, while the Mega cycle moves the slower half. During Phase 1, roughly half the market remains optimistic, so valuation alone is judged unlikely to force a crash larger than 30%.
 
The 2026 Live Overlap
Phase 1 of Hansen's Mega Sentiment Cycle—the long inner–outer angle from 0° up to the next AFP at 90°runs from autumn 2022 until the first 90° column of 2026, projected for late April–May, with peak geometry-driven euphoria in late May, a second lift by early August, and a third close in early December. A moderate M-Spike overlaps the first column, making April–June the unstable hinge.
 
The chart (December 06, 2024 to January 01, 2027) shows the US stock-market price level (log) through July 18, 2025—the analysis date—along with the drivers of the three 90° configuration events comprising the 2026 Anxiety-Free Period and the M-Spike as of June 2025. Forward map showing the three 2026 AFP columns, overlapping M-Spike, May peak, and June hinge. US Stocks refers to the DJIA, S&P 500, or related ETFs. 
2026 AFP Map and the Boom-Then-Fade Hypothesis 
Hansen's sketch is: enter several weeks before an AFP, hold through the cluster high, exit on the Micro Market Resilience Index; he prefers equal-weight S&P 500 or the DJIA as cleaner sentiment gauges. That is a multi-month calendar, not a daily trigger and not proof that high valuations cannot break.
 
2026 is one such labeled window: three separate 90° columns, not a continuous anxiety-free bid into year-end. The first and strongest was late April–May (peak late May). An overlapping M-Spike made April–June the hinge—historically a dip zone, not a melt-up. A weaker second lift was dated August–September. The third column, late November–early December, ends the cluster; Hansen's average script is a boom during the bars and about −13% after the peak. 2006 barely rose, so an AFP is not a guarantee of higher prices. November–December is the close of the episode, not "anxiety-free until Christmas."
 
Use that map to watch whether price, Ap, sunspots, and standing-wave stability follow the boom-then-fade pattern. For next-week risk keep short-horizon Ap/Kp and real-time L1 solar wind—those still have skill. The Schumann link rests on one AFP and R20.05R^2 \approx 0.05; 2026 is the live joint test of cavity-mode coherence, solar-metric co-movement, and that price script. Do not size as if the mechanism were already proven. Hansen's paper is research, not investment advice.
 
Reference:
Jeffrey A. Hansen is founder of CPM Investing LLC and an asset-allocation researcher who began in geophysics and natural-resource exploration, later evaluating quantitative investment managers at Russell Investments, advising investment firms on technology adoption and product development, managing global multi-asset funds at Nikko AM America, and since 2015 specializing in asset-allocation research and ETF model portfolios for individual investors. 
S&P 500 vs. Hansen's "Micro Driver" (data input and formula undisclosed), digitized from the weekly chart in his August 7 forecast above and plotted against the daily S&P 500 for clarity. The "Micro Driver" path shows rising prices into Sep 4 (Fri), a trough around Oct 2 (Fri), followed by a higher peak around Oct 16 (Fri), a trough on Nov 27 (Fri), and a weaker bounce into Dec 25 (Fri).
Hansen Anxiety-Free Periods 1933-2051
The model uses two planetary centers of gravity: the Inner Orbital Center, a weighted mix of Mercury, Venus, Earth, Jupiter, and Saturn, and the Outer Orbital Center, a weighted mix of Jupiter, Saturn, Uranus, and Neptune, with a line from the Sun to each center. Hansen's AFP clock is simply how close the opening angle is to a right angle. He counts a "column" when it falls between 86° and 94°. Because the inner planets move quickly, the angle wobbles in and out of the band, so an AFP is usually a handful of orange bars or columns spread over a few months, not one solid year. To calculate Hansen's Anxiety-Free Periods through 2051, his published weights and NASA/JPL planetary positions were used.

Hansen AFPs, 1933–2051: Orange columns mark weeks of Anxiety-Free Periods, when the Sun–vertex angle between the inner (Mercury–Saturn) and outer (Jupiter–Neptune) planet-group centers (black curve in the lower panel) falls within the 86°–94° band; column height quantifies the number of weeks within the band. The upper panel overlays these periods with a black line showing detrended DJIA weekly closing values. Looks pretty random. Hardly something to bet the farm on. 
Hansen 
Anxiety-Free Periods (2026–2051).
 
There are 16 clusters from 1935 to 2051. After the current 2026 AFP, the next full cluster is November 2032–July 2033. Then comes a long empty stretch: the angle falls toward 0° (the two centers lined up) and does not re-enter the band until a weak July 2050 graze and a full 90° column in January 2051. Gaps with no AFPs are 2027–31 and 2034–49. 
 
The 2026 Live Real-World Test: Respect Uncertainty. Never Bet the Farm
The orange AFP columns are a real, rebuildable orbital clock. However, they are not a price clock. The Dow's detrended path already has its own slow waves—wars, inflation, bubbles, QE. An AFP arrives roughly every 7–13 years, so some columns will naturally land near highs, selloffs, or dead middles. That happens with or without the 90° angle doing anything. 

Hansen's stronger claim is window timing. But his sample is only thirteen episodes: +28% on average, followed by −13%, with durations matched to extreme percentiles. And the misses matter: 2006 barely moved; 1937 and 1987 were ugly. The proposed chain—stable Sun → ionosphere → Schumann → mood—still rests on a tiny Schumann window and an R² ≈ 0.05. Micro Driver, M-Spike formulas unpublished, with p ≈ 0.19. So 2026 is a real-world test, not proof that the theory works. The geometry can be projected to 2051. Trader psychology cannot.

Right now, AFP 2 runs through roughly September 18; a possible market low comes in early October; AFP 3 lands in late November–early December, followed by the fade. If 2026 fails to deliver the usual boom-then-fade against this tape, that failure is the evidence. If it rhymes, fine—but it is still one more cluster, not a law. Watch the timing window. Respect the uncertainty. Never bet the farm on orbital geometry.
 
See also:

Saturday, August 22, 2026

S&P 500 vs. Ap Index: +3-Day Lag and Limits of Multi-Week Forecasting

The chart below illustrates the hypothesis that geomagnetic activity, measured by the planetary Ap index, precedes trend reversals, as geomagnetic disturbances subtly impair collective mood and increase risk aversion. This idea draws on research examining correlations between space weather and financial markets, including evidence of both direct and inverse relationships between Ap—and related Kp and F10.7—readings and subsequent market performance.

S&P 500 vs. Ap Index (Apr-Oct 2026). Projected Ap peaks:
Sep 4 (Fri),  Sep 17–20 (Thu-Sun), Oct 1 (Thu). 
 
Chart Construction and Data Sources
The chart overlays the daily S&P 500 with the Ap index shifted forward by three calendar days—the short lag that currently offers the best balance between the classic weekly effect reported in the literature and practical S&P 500 trading-day alignment. The series is then extended using the NOAA 45-day Ap forecast. Historical daily Ap data are sourced from GFZ Potsdam, while the dashed forward segment represents the latest NOAA SWPC 45-day Ap forecast, issued on August 22, 2026. 
 
Limits of the NOAA 45-Day Forecast for Forward Correlation
However impressive the historical correlation may appear, its reliability as a guide to future relationships is inherently limited. NOAA's 45-day Ap forecast is a relatively low-resolution space-weather projection, it is adjusted on a daily basis, and its predictive skill declines rapidly beyond the first week. Moreover, the forecast activity levels shown in the chart are modest (Ap 8–15) and remain well below classic geomagnetic storm thresholds: Ap 8–15 corresponds roughly to Kp 2–3 (quiet to unsettled conditions), while Ap 48 corresponds to Kp 5, the threshold for a NOAA G1 geomagnetic storm. 
  
Latitude-Dependent Solar Rotation and Active-Region Return Times
Sunspots and active regions do not return to the Earth-facing side of the Sun on a fixed schedule. Because the Sun rotates differentially—faster at the equator (~25 days sidereal, or ~27 days synodic as seen from Earth) and progressively slower at higher latitudes (reaching ~30–35 days near the poles)—the time required for a given region to reappear depends on its heliographic latitude. The standard Carrington frame uses a compromise rotation period of 27.2753 days (synodic), which roughly corresponds to the typical 10–20° latitudes of sunspots. Regions at higher latitudes therefore take longer to rotate back into view, while those near the equator return sooner. 
 
Solar Activity Snapshot: Comparing Sunspot distribution on the Earth-facing and far sides of the Sun (August 22, 2026).
 
From above the Sun's north pole, its rotation is counterclockwise, carrying sunspots from left to right.
 
Reading the Raben Earthside and Farside Maps 
The Raben maps above illustrate this directly: The Earthside view shows currently visible active regions, identified by NOAA numbers and activity-color coding, while the Farside view highlights returning regions with meridian lines estimating the number of days until they may reappear, assuming a uniform rotation rate. In reality, those return times can stretch or compress with latitude. A high-latitude complex visible on the farside today, for example, may take several additional days to rotate back into Earth view compared with a low-latitude region. 
 
How Returning Regions Drive F10.7 and Ap
These returning regions influence both the 10.7 cm radio flux (F10.7) and geomagnetic activity (Ap and Kp). F10.7 serves as a direct proxy for solar EUV/UV output associated with active regions and plages; when a large active complex rotates onto the Earth-facing disk, F10.7 typically rises. Ap, by contrast, responds more indirectly: high-speed solar-wind streams from coronal holes, as well as coronal mass ejections launched from Earth-directed active regions, can disturb the magnetosphere and elevate the planetary Ap index. 
 
Construction of the 27-Day and 45-Day NOAA Forecasts
Consequently, the 27-day forecast for F10.7 and the geomagnetic Ap and Kp indices and the 45-day Ap/F10.7 forecast issued and updated daily by NOAA SWPC, are both built around the expected recurrence of these features through solar rotation. The 27-day forecast is essentially a recurrence forecast, assuming that active regions and coronal holes will reappear roughly one Carrington rotation later. The 45-day forecast extends this approach farther into the future, blending recurrence-based estimates with a longer-term background trend.
The time a Coronal Mass Ejection (CME) takes to reach Earth depends mainly on its density and solar-wind conditions:. fast CMEs (>1,000 km/s) arrive in 1–2 days, average CMEs (500–1,000 km/s) in 2–3 days, and slow CMEs (<500 km/s) in 3–5 days.
The Moon's orbit through Earth's magnetosphere, and the corresponding reduction in solar wind ion flux as it enters the magnetotail cavity near full Moon (0°), provides one example of how the solar wind–magnetosphere configuration can influence geomagnetic conditions. More broadly, the semiannual variation of geomagnetic activity is linked to the interaction between the solar wind and Earth's tilted magnetic field, which typically causes increased geomagnetic disturbances around the equinoxes and lower activity around the solstices.
Why Multi-Week Ap Forecasts Remain a Coarse Guide
That is precisely why attempts to forward correlate 27-day and 45-day Ap forecasts with the S&P 500 are inherently limited. The Sun's differential rotation, the uncertain evolution of active regions—including their growth, decay, or disappearance while on the farside—the variable geoeffectiveness of individual regions, and the chaotic nature of solar-wind–magnetosphere coupling all erode day-to-day predictability.  
 
 
Hence, multi-week Ap and F10.7 forecasts should be interpreted primarily as defining a broad solar-activity envelope rather than as precise day-by-day projections capable of supporting a tight forward correlation with daily S&P 500 returns. By contrast, short-horizon tools—such as the NOAA 3-day forecast, the LSTM-based 72 hour Ap predictor, and real-time L1 solar-wind dataretain greater predictive value for near-term market conditions.
  
See also:

Friday, May 1, 2026

Federal Funds Rates & Solar Activity: Projection through 2031 | Vladimir Belkin

The present study compares the serial years of the average solar cycle with the arithmetic mean values of the effective US Federal Funds Rate for the period 1955–2025. 

Serial Numbers of Solar Cycle years (1 to 13) and Federal Funds Rates (%) projected through 2031. 
 
[...] The correlation between the serial number of solar cycle years and average Fed rates is extremely strong, with coefficients reaching -0.999 during years 5–7 and 0.994 during years 1–5. The serial number for the year 2026 in the current Solar Cycle 25 is 7. [...] Consequently, the forecasted Fed rate for 2026 is [...] 3.052%. The forecasted Fed rate for 2027 is [...] 3.558%
 
[According to Belkin's methodology, the Fed rate should rise and peak in 2029 at around 5.5%.]

Reference:
Vladimir A. Belkin (January 1, 2026) -  Federal Funds Rates and Solar Activity (1955–2025): Evidence of a Very High Correlation.
[СТАВКИ ПО ФЕДЕРАЛЬНЫМ ФОНДАМ И СОЛНЕЧНАЯ АКТИВНОСТЬ (1955-2025): ДОКАЗАТЕЛЬСТВО ОЧЕНЬ ВЫСОКОЙ КОРРЕЛЯЦИИ.
[Note: As of May 1, 2026, the Federal Reserve has set the target range for the federal funds rate at 3.50% to 3.75%., with the most recent daily effective federal funds rate (EFFR) recorded at 3.64%.]

Wednesday, January 21, 2026

"Does the Son of the Dust Know Anything More Beautiful?" | Einar Ben

Following the intense Northern Lights displays triggered by a G4 geomagnetic storm on January 19, 2026, forecasts now predict a Kp index of 4 for January 21. These auroras are currently visible across Iceland, Greenland, and the northern parts of Scandinavia, Russia, Canada and Alaska.
 
 Iceland, January 20, 2026.
 
» Does the son of the dust know anything more beautiful
than the palace of gods in electronic flames?
By the universe bosom everything is fire
and decoration of slithering northern lights.
From the seventh heaven to the ocean’s horizon... «

Thursday, December 19, 2024

Ap Index of Geomagnetic Activity and S&P 500 Returns | Lifang Peng et al.

Lifang Peng, Ning Li, and Jingwen Pan (2019) test whether the monthly planetary Ap index, used as a proxy for disturbed geomagnetic days, is associated with S&P 500 returns over January 1998–December 2017.    

High AP Index, low stock market performance—really?
 
The working hypothesis is behavioral rather than mechanical: geomagnetic disturbances have been linked to poorer sleep, mood, and health, which can raise risk aversion and reduce demand for equities. The authors therefore treat Ap as an environmental mood shock and ask whether that shock shows up in US index returns after standard market controls. Data come from NOAA for Ap and from a standard US equity series for the S&P 500; the analysis is monthly, not daily, which reduces noise but also blunts short-horizon storm effects.

The core result is a statistically significant inverse relationship: higher monthly Ap is associated with lower S&P 500 returns. Granger-style tests and regressions with year dummies support a directional link from geomagnetic activity to subsequent market performance rather than the reverse. The economic magnitude is small. The authors describe an adverse-signal probability on the order of 1.2 per thousand, so Ap is a detectable but not dominant driver. Liquidity matters: the negative Ap effect is stronger when market liquidity is higher, which they interpret as faster transmission of mood-driven order flow through more liquid books. This is the paper's most distinctive empirical claim relative to the earlier weekly-storm literature of Krivelyova and Robotti.

A second distinctive finding is seasonal. Long-term Ap has well-known spring and autumn peaks (the Russell–McPherron / equinoctial pattern). Prior work often attributed geomagnetic–return links to that semiannual cycle. Peng et al. argue that the Ap–S&P 500 association in their sample is not mainly an artifact of those equinoctial maxima. After allowing for seasonal structure, the inverse relationship still appears, which they take as evidence of a more general geomagnetic channel rather than a calendar-season dummy in disguise.

The contribution is therefore modest but clear: it brings a standard space-weather index (monthly Ap) into an econometric study of US equity returns, documents a negative and liquidity-amplified association, and rejects a purely semiannual explanation. It does not establish a tight causal mechanism, does not use daily or storm-threshold specifications, and does not claim usable short-horizon forecast skill. 

 
The semiannual variation of geomagnetic activity is linked to the interaction between the solar wind and Earth's tilted magnetic field, which typically causes increased geomagnetic disturbances around the equinoxes and lower activity around the solstices.

Tuesday, December 17, 2024

Strong Inverse Correlation between Ap Index and Gold Price | Vladimir Belkin

A strong inverse correlation (coefficient -0.7879) between the geomagnetic Ap Index and the gold price, with a one-year lag, is observed over 57 years of data.
 
 Strong inverse correlation, with a one-year lag—seriously?
 
Based on the results of his study, the author predicts a significant decline in the price of gold in 2024.
 

 Gold (weekly bars) – January 1 to December 17, 2024: +28%.