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.  

 

KMAS 3- and 7-day solar wind forecast based on ACE observations.

GFZ high resolution 3-day forecast of ap30, ap60 and ap indices.

 

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 data—retain greater predictive value for near-term market conditions.

  

See also:

Jeffrey A. Hansen (2026) - Physics-Based Forecasts of Investment Sentiment. 

Vladimir Belkin (2024) - Strong Inverse Correlation between Ap Index and Gold Price.  

Lifang Peng et al. (2019) - Ap Index of Geomagnetic Activity and S&P 500 Returns. 

Anna Krivelyova & Cesare Robotti (2003) - Playing the Field: Geomagnetic Storms and the Stock Market.

2026 High in the Benner Cycle | "Time to Sell Stocks and Values of all Kinds"

Samuel Benner (1832–1913), a once-prosperous farmer in Lawrence County, Ohio, whose wealth was destroyed by a devastating hog cholera epidemic and the Panic of 1873, devoted the remainder of his life to identifying recurring patterns in economic booms and busts. Through exhaustive analysis of commodity prices—specifically provisions (pork products such as bacon, ham, mess pork, lard, and salted pork), live hogs, corn, cotton, and pig iron (later also wheat and railroad-stocks)—he published "Benner's Prophecies of Future Ups and Downs in Prices" in 1876, a work that formed the basis for his annual forecasts through 1907.

  

 » Periods When to Make Money. « The original 1872 business card of the George Tritch Hardware Co. in Denver, Colorado—which was copyrighted in 1883 and 1897—is the focus of an ongoing controversy: Was it genuinely created by Tritch, and simply plagiarized and popularized by Benner four years later in 1876?

 
Benner’s approach was empirical, grounded in price data from 1780 to 1872, and used to extend projections far into the future by emphasizing recurring cycles in commodity prices and business activity. He treated these cycles not merely as descriptive patterns but as prescriptive guidance, advising investors on when to buy during "hard times" and when to sell during "good times."

 

Benner's time-price model identified nested peaks and troughs in commodity prices, agricultural yields, and broader economic conditions. Central to his framework were the following patterns:

■ 27-Year Cycle in Pig Iron and Cotton Prices: Analyzing data from 1833 to 1899, Benner observed high prices following an ascending arithmetic progression of 8, 9, and 10 years, repeating every 27 years. Low prices, conversely, followed a descending series of 9 and 7 years. This cycle captured the volatility in industrial commodities like pig iron, which Benner viewed as a bellwether for economic health, given iron's role in manufacturing and infrastructure.
■ 11-Year Cycle in Corn and Hog Prices: Beginning in 1836, this cycle alternated between 5- and 6-year sub-periods, reflecting fluctuations in agricultural staples. Benner broke it into peaks and troughs that aligned with seasonal and weather-related disruptions.
■ Business Cycle with 16-18-20 Year Peaks: Extending his commodity analysis, Benner described a broader 11-year business rhythm, characterized by peaks spaced 16, 18, and 20 years apart. Lows coincided with pig iron troughs, while panics occurred at intervals averaging 9 years (7-11-9 pattern, akin to the Juglar cycle). Every third peak aligned roughly every 54 years, echoing longer waves like those later formalized by Nikolai Kondratieff.

 Benner's astronomical time-price cycles theory.

These cycles formed a hierarchical structure: shorter oscillations (5–11 years) drove immediate price swings, while longer ones (27 and 54 years) shaped multi-decade eras of prosperity or contraction. Benner integrated them into a single chart, forecasting "ups and downs" with directives such as "Years of Good Times: High Prices and the Time to Sell" for peaks and "Years of Hard Times: Low Prices and a Good Time to Buy" for troughs.

 

 

 » "B." [2026] Years of Good Times. High Prices and the Time to Sell Stocks and Values of All Kinds. « 

For 2025, Benner’s cycle predicted the US stock market driving higher; for 2026, it forecasts a major top: "High Prices and the Time to Sell Stocks and Values of All Kinds" into 2032 ("Years of Hard Times, Low Prices, and a Good Time to Buy Stocks"). 2026 is marked as a "B" phase year — a peak of high prices and euphoria, often the culmination of a bull market before a shift to downturns. Historical "B" peaks have aligned (often within 1-2 years) with major tops like: 1929 (Great Depression peak), 2000 (dot-com bubble), 2007 (pre-2008 crisis), and others. 

Benner attributed these periodicities to celestial mechanics, positing that solar system dynamics influenced earthly economies. He aligned his 11-year cycle with Jupiter's major equinox, which recurs every 11.86 years—a near-match to observed corn, hog, and business fluctuations from 1836, 1847, 1858, and 1869. Jupiter, in his view, served as the "ruling element" in natural product price cycles, potentially modulated by electromagnetic influences from Uranus and Neptune on Saturn and, in turn, Earth.

This astro-economic perspective echoed earlier hints by English economist William Stanley Jevons, who suggested in 1843 planetary configurations might underpin business cycles but abandoned the idea amid academic opposition. Modern interpretations extend this to lunar phases and solar activity (e.g., nodal precession, sunspot cycles), though Benner's original emphasis remained on observable price data rather than strict astronomy and astrology.

   

Benner's Cycle Forecast for the Period 2015–2035.

In 1948, Edward R. Dewey, director of the Foundation for the Study of Cycles, updated and reprinted Benner’s work as the Foundation’s "Reprint No. 24". He lauded Benner’s pig-iron forecasts over the 60-year period from 1875 to 1935 for achieving a gain-to-loss ratio of 45:1, deeming it one of the most reliable business charts despite numerous imitations by lesser-known authors. Proponents cite alignments with major events: the cycle's "B" peaks (high-price euphoria phases) approximated the 1929 stock market top preceding the Great Depression, the 2000 dot-com bust, and the 2007 pre-financial crisis summit—often within 1–2 years. 

 

Edward R. Dewey (1967) considered the true length of Benner’s pig iron price cycle to be 9.2 years and thus his "forecast got off the track by one year every five waves. By 1939 his projection was no longer usable."  In 1971 Dewey commented: "Were Benner still alive and issuing yearly supplements to his Prophecies, he probably would have learned all that was necessary to know about cycles of fractional length and would have adjusted later forecasts accordingly." 

However, scrutiny reveals nuances: Benner's original chart, rooted in agriculture (which comprised 53% of the US economy in the 1870s), projected a 1927 high and 1930 low, not the exact 1929–1932 Depression timeline. A sensational 1933 Wall Street Journal article, designed to attract attention, altered Benner’s original cycle dates for dramatic effect, thereby fueling persistent misconceptions (see chart below).

 

 

Martin Armstrong recently contended that Benner’s cycle was more a historical curiosity than a reliable predictive tool, noting that it has been both right and wrong many times: 

 

The claim that Benner’s Cycle predicted the Great Depression is false. The chart [above] that was published in the Wall Street Journal altered Samuel Benner’s cycle, which was based on agriculture. It predicted a high in 1927, not 1929, and the low in 1930, not 1932. Claims that Benner’s work calls for a crash in 2025 are flat-out wrong. His target years would be 2019 and 2035, based on his data, not the altered, fake news published by the Wall Street Journal in 1933.

 

Benner was a farmer. Applying his cycle to the economy today is no longer effective, any more than the Kondratieff Wave. Both were based on the economy, with agriculture being the #1 sector. As the Industrial Revolution unfolded, those cycles remain relevant for commodities, but not the economy. Agriculture, when Benner developed his model, accounted for 53% of the economy. Today it is 3%. If they were alive today, they would have used the services industry. Capital flows are still pointing to the dollar, given the prospect of war and sovereign defaults outside the USA.

Martin Armstrong, August 30, 2025.

 

See also: 

Samuel Benner (1876)  - Benner's prophecies of future ups and downs in prices. 

What years to make money on pig-iron, hogs, corn, and provisions.  

Samuel Benner (1907)  - Benner's prophecies of future ups and downs in prices. 

Edward R. Dewey and Edwin F. Dakin (1947) - Cycles: The Science of Prediction.

Edward R. Dewey (1967)  - The Case for Cycles.
Edward R. Dewey and Og Mandino (1971) - Cycles: The Mysterious Forces that Trigger Events.

LCdr. David Williams (1982) - Financial Astrology.  

TPR (2022) - "Periods When to Make Money": Benner Cycle Projection into 2023 Major Low.

Fed Cuts, Banks Cash In, Main Street Bleeds, Stocks Rise | Oscar Carboni

Jerome Powell cut rates by a quarter point. Big deal? Not for Americans paying 8% mortgages. Banks borrow from the Fed at 4% and lend at nearly double. Every cut fuels their spread, no relief for homebuyers. Bond market moves by banks erase any Fed benefit.

» Every time the Fed lowers rates, banks push down the bond market, which drives mortgage

rates right back up. We saw this earlier this year: bonds get hammered, rates climb. «

 

Main Street loses. Wall Street profits. This loop has repeated for months. Powell’s cuts can’t counteract bond manipulation. And the bigger risk looms: in past crises—2008, COVID—near-zero rates saved the system. Burn through cuts now, and the Fed has less firepower when the next shock hits.

» Bonds don’t look good, but the S&P, NASDAQ, Russell, Bitcoin, even real estate—all look strong.

Lower rates push asset prices higher. So we’ll trade dips, especially in Bitcoin, and ride the trend. «

Traders, however, see opportunity. Even tiny rate cuts flood liquidity into markets. Equities, crypto, real estate—they all get a boost. S&P, NASDAQ, Russell, Bitcoin—buy dips, ride the rally. Bonds remain toxic, but risk assets thrive. Cuts inflate prices, but housing stays out of reach.

The solution is simple: cap lending spreads. If banks borrow at 4%, mortgages shouldn’t exceed 6%. Without it, the Fed's moves only fuel asset inflation while Main Street bleeds. Until reform arrives, liquidity drives traders’ gains while banks run the bond market—and Americans pay the price. The Fed may cut, but the real game is elsewhere.

Reference:

Oscar Carboni (September 18, 2025) - Bond Market, Banks & Jerome Powell's Interest Rate Move Explained. (video)

 

» When the Fed cuts with the S&P <2% from ATH (13x since ’90), the next 30 days is a coin flip (6 up/7 down).  3-months out has almost a perfect record: 12/13 up with the last and only loss in 1990. Recent four 3-month gains: +6.2%, +5.9%, +7.7%, +1.6%. «
Mark Minervini, September 19, 2025.

 

See also:

Alex Krainer (September 20, 2025) - How Rate Cuts Fuel an Overheated Market,

and Why a Pullback Is Part of the Journey to new Highs. 

TPR (September 16, 2025)  - “Sell Rosh Hashanah, Buy Yom Kippur” | Hurst Cycles Suggest Otherwise. 

 Jeff Hirsch (September 9, 2025) - September Seasonality of US Stock Indices.

Chinese Stock Indices, Gann Time Theory & Solar Terms | Tianbao Zhou et al.

Stock indices proved to be rather predictable to some extent. Therefore, according to the study, investors can invest in ETFs that belong to the indices as an ETF is completely coincidental with the index it belongs to. Furthermore, ETFs provide investors with a variety of options of risk and profit. The Shanghai ETF is smooth whereas the Second Board 50 Fund fluctuates a lot. Investors are able to get a high profit from individual stocks as well through implementing the results of this study. The correlation between the turning points of indices and the Chinese 24 solar terms was positive (r = 0.9878).

Turning points always occur near solar terms. Through testing n-day extreme points with a different n value, the sharp turns of the trend often happened near the solar terms, and if we choose 4 days as the valid time radius, the probability is about 80%. Investors should be alert for four days before and four days after a solar term. If the price is too high (low), it is more likely to be affected by the coming solar term, and the higher (lower) the price is, the more instability the trend then would have. However, solar terms are not always strong turning points, but they might cause weaker turning points. In other words, solar terms might not cause a sharp reversal of the stock trend; strong turning points were just some exceptions. Usually, the turning points were not that strong but sufficient for medium-term and short-term investors. The alert period provided investors with a good strategy for short-term and medium-term trading. When judging the upcoming reversal, it should be dynamic. 

 

 

[...] Eight of the Chinese 24 solar terms are very prominent, namely, Chunfen (6), Xiazhi (12), Qiufen (18) and Dongzhi (24), which represent the most vigorous time-points in each season and are the most important four solar terms; the other four are Lichun (3), Lixia (9), Ligiu (15) and Lidong (21). These four represent the beginning of each season and are the second important four solar terms.

 

To our surprise, the importance of these eight solar terms exactly coincides with the wheel of the cycle theory in Gann theory. In Gann’s wheel, the most important four angles are 90°, 180°, 270° and 360° (0°), and the corresponding time-points of each year are exactly the four solar terms of Chunfen (6), Xiazhi (12), Qiufen (18) and Dongzhi (24). The second important four angles, 45°, 135°, 225° and 315° exactly correspond to the four solar terms of Lichun (3), Lixia (9), Liqiu (15) and Lidong (21). Regardless of the angle in Gann theory or solar terms, they all point to a common rule, that is, the stock trend is most likely to turn at these eight points. We can summarize the above results as follows: variable or more significant extreme points often occur at the solar term point, and the solar term point usually makes the stock trend turn according to its strength, and the turning strength is large or small.

 

[...] the Chinese traditional culture, human society is affected by natural factors at every moment, and one of the factors is time (including the time cycle, time-points and time periods). Despite the fact that the absolute price of a stock is generally supposed to be unpredictable, the turning points and reversal of trend of stock indices have rules to follow. 

 

Gann theory suggests that the cycle of time is almost everywhere in the stock market, like our pulse cycle and four seasons of the year. Nobody denies the existence of the time cycle as it retains its rationality and regularity in the nature. Whether or not we know, the regular shocks and vibrations in the stock market caused by time do happen.

[...] we only analyzed the trend and turning points of the Shanghai Index rather than a certain stock or an absolute stock price. We supposed that the index is a wide and general performance of the stock market which eliminates many extreme and irregular cases. Many theories have focused on calendar effects, and all of them show the effort in searching for the independent time factors over regular human factors that may affect the stock market. However, such a division of time is so modern that the turns do not always fall on them. 

 

Besides the solar terms, in China, we have 12 zodiacs (corresponding to a 12-year cycle), lunar months (corresponding to the monthly change of the moon), 10 heavenly stems and 12 earthly branches as well as the constellation of both the Chinese version and the Western version. Thus, we can see that throughout the history, ancient people were always doing tremendous work in summarizing many kinds of time cycles in order to survive, forecast and develop their civilization.

 

As early as the Spring and Autumn Period (770–476 BC), Chinese ancestors had already established two major solar terms, ri nan zhi (日南至 'Sun South Most') and ri bei zhi (日北至 'Sun North Most'). As of the end of the Warring States Period (475–221 BC), eight key solar terms (Start of Spring, Vernal Equinox, Start of Summer, Summer Solstice, Start of Autumn, Autumnal Equinox, Start of Winter and Winter Solstice) marking the four seasons, were established according to the different positions of the sun and changes in natural phenomena. The rest of the solar terms were initiated in the Western Han Dynasty (206 BC–24 AD). Hence most terms refer to the climate of Xi'an, capital of the Han Dynasty.

[...] The 24 solar terms in each year and their links accurately fitted the trend of the stock in that year. Using 24 price data-points instead of nearly 250 daily data-points of the whole year could make the daily data of high frequency more concise and easier to process. With 250 high-frequency daily data-points, there is strong volatility, which leads to the obvious heteroscedasticity of the data and increases the complexity of data analysis. 

 

The use of 24 solar terms instead of annual data also greatly reduces this unstable and irregular fluctuation. This also coincides with Gann theory. The forecast of future trends in the all-terms group and the eight-terms group was precise, but there remained a gap with the absolute price. We were only able to forecast the time-points and the turning points; as for the absolute price, we hardly made it. This is because the stock market involves a great deal of instability and is extremely complicated.

[...] as we were inspired by Gann, Elliott and the Chinese 24 solar terms, we would rather look for those that do not change, and that is the key to have a better understanding and cognition of our real world, of course, including the stock market. For this reason, it is the higher dimensional time factor and time cycle that produce an overwhelming impact on the stock market, so it reminds us of taking into account the importance of time when conducting such a study. That is why Gann summarized a tremendous amount of time periods to inform the possible reversal in the capital market while the ancient Chinese figured out 24 divisions of a year as 24 solar terms which all solely point to time.

In addition, the ancient Chinese elaborated a complex system, and there are actually many  other divisions of time, years, months, etc. in the Chinese culture. For example, the ten heavenly stems and the twelve earthly branches decide what a year would be like, and that is a 60-year cycle as there are 60 different combinations of one out of the ten heavenly stems with one out of the twelve earthly branches. By the way, one combination is called Gengzi, which is supposed to be the year of disasters and conflicts; the latest Gengzi year was 2020.

Quoted from:
Tianbao Zhou, Xinghao Li & Peng Wang (2021) - Statistics and Practice on the Trend’s Reversal and Turning Points of Chinese Stock Indices Based on Gann’s Time Theory and Solar Terms Effect. 

 

See also:
W.D. Gann (1949) - 45 Years in Wall Street.

W.D. Gann (1954) - Master Commodities Course.

Robert R. Prechter Jr. (1994) - R.N. Elliott's Masterworks.

Ray Tomes (2010) - W.D. Gann's Natural Trading Days.

TPR (2012) - Gann's Natural Trading Days.

TPR (2019) - S&P 500 Index vs Division of Solar Year 2020 starting from Earth’s Perihelion. 

Wikipedia (2022) - Solar Term.

ChineseCalendarOnline.com (2022) - The 24 Solar Terms.

 National Astronomical Observatory of Japan (2022) - 24 Solar Terms.

 

Date and Time Information of 24 Solar Terms in 2018, 2019, 2020 and 2021