https://www.edgarepeters.com/blog-2-2 daily 0.75 2025-02-09 https://www.edgarepeters.com/blog-2-2/introduction monthly 0.5 2023-10-06 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/da571a97-fea5-4a06-bbbc-def5471de762/IMG_0100.JPG Hypertext Book - Introduction - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/3703bd90-293b-4f43-8b3d-f02b274a5ed3/MUSI+spaghetti+graph.png Hypertext Book - Introduction - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.edgarepeters.com/blog-2-2/market-climatology monthly 0.5 2023-10-09 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/6b2da692-e9eb-47ec-8921-be11f1c7dd9a/hurricane+seen+from+space+in+the+style+of+van+gough.png Hypertext Book - Market Climatology - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661880263604-W17GGEDZ1WM257LVLWHY/El+Nino+time+series.png Hypertext Book - Market Climatology - Make it stand out The Southern Oscillator over time. Note the long time periods to complete a cycle. (By Rainald62 - Own work, CC BY-SA 3.0) https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661871376537-SRNZB9PLE9SEX6FYZVOU/La_Nina_regional_impacts.gif Hypertext Book - Market Climatology - Make it stand out Regional Impact of La Nina. Source: NOAA https://www.edgarepeters.com/blog-2-2/blog-post-title-one-sf2m5 monthly 0.5 2023-10-06 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661366497863-RQUCIGLNEUJQAVR9YY55/FMA.jpg Hypertext Book - The Fractal Market Hypothesis: An Overview - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661515320059-QFXA8E1CC8U2H7FBADJT/Lung.jpg Hypertext Book - The Fractal Market Hypothesis: An Overview - You might ask, “What’s fractal about this?” One thing about fractals is that they have no characteristic scale. For example, the human lung has a main branch, the trachea, and then multiple branching generations off of that main branch. The average diameter of each generation scales down according to a power law. And while the average diameter branches according to a power law, each branching generation actually contains a distribution of diameters around that average. So each branch within each branching generation is different that the others. This diversified structure is more resilient during formation than if the lungs generated according to a characteristic scale such as each branch being half of the previous branch. Why? If one branch were too large or small during development, that error would continue through the rest of the branching generations and the lung would likely fail. By spreading the error without a characteristic scale, the lung formation process is more resilient to shocks. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661708170657-9SHGGL90T2G1RR1V0OIW/Kristoufek+graph.png Hypertext Book - The Fractal Market Hypothesis: An Overview - This graph from L. Kristoufek’s paper “Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence” (Scientific Reports 2013) shows the wavelet power spectrum for the NASDAQ index from March 1 2000 - May 30 2013. The top graph shows the frequencies of each trading day. The hotter the color the higher the frequency. We can clearly see the tech bubble period from 2000-2003 where higher frequencies dominated and again in late 2008 - early 2009 during the Global Financial crisis. During other periods no frequency dominates. Both conditions are predicted by the FMH. Kristoufek also shows this same analysis for several other non-US indices for the same period. https://www.edgarepeters.com/blog-2-2/what-chaos-theory-teaches-us monthly 0.5 2023-10-09 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1660663284190-ZTQSUT7WE8LJRU75E8N8/Lorenz+attractor.png Hypertext Book - Chaos Theory, Market Cycles and Macro Regimes Chaos Theory The market system is actually simpler than it looks, but also being quite complex, and it relates to chaos theory. It sounds like a joke to say the market is chaotic (duh!) but in chaos theory a system can look random but be completely deterministic. And a chaotic system can have multiple dimensions which also look unrelated to one another though they are directly tied. Trying to understand one dimension without taking into account the others is a losing game. Look at a well known chaotic attractor, the Lorenz attractor. It’s one of the poster children of chaos theory and usually shown in two dimensions so it looks like owl eyes. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661431483676-IXFEZD793VIP0IBZULSR/lorenz2.png Hypertext Book - Chaos Theory, Market Cycles and Macro Regimes - While two of the series, x and y, look very similar to one another, the third one, z, looks completely different. In fact, x and y have a 60% correlation with one another but have correlations of 1% and -2% respectively with z. If you look at x and y they spend a fair amount of time either above or below the zero line. In the “owl eyes” graph this is when the system shifts from one eye to the other. That shift is largely caused by z which looks statistically unrelated to x and y. So it would be easy to overlook z if we didn’t know there was a direct link. We can think of x, y, and z as following their own cycles. Cycles are when x, y and z go up and down. But x and y also have regimes, periods of time where they are above or below zero. x and y also show you the nature of “non-periodic cycles.” A periodic function like a sine wave would go above and below the zero line with great regularity. If we were to measure a cycle length from peak to peak they would always be equal which defines a “periodic” cycle. But x and y spend different times above and below zero and also from peak to trough. The regimes are of different lengths as are the cycles, but they do have an average length. This is similar to the investment horizon length I use in the Fractal Market Hypothesis. https://www.edgarepeters.com/blog-2-2/cycles-vs-regimes monthly 0.5 2023-12-16 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/c1be23da-9a8b-4c14-825c-27764caf1090/Phases+of+the+moon+in+an+arc.png Hypertext Book - Market Cycles vs. Macro Regimes - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661516400830-OU5BLK8KPRF3OIRVV0JD/Global+Temp+over+time.gif Hypertext Book - Market Cycles vs. Macro Regimes - One way to think of cycles vs. regimes is to look at climatology. The seasons, as we know, are defined by the tilt of the Earth towards and away from the sun. We have vernal and autumnal equinox dates to define when the seasons change. Characteristics change as the seasons change including temperature and precipitation. The full seasonal cycle covers the time that the Earth circles the Sun which defines one year of time. But around this are longer periods generally termed as “ages” which last for centuries when the overall average temperature of the earth changes. This affects the seasons but during these ages the seasons persist as the Earth continues to tilt on its axis towards and away from the Sun. The nature of each seasonal cycle changes appreciably within the age but they continue. The cause of the longer age can vary over time. Sometimes they’re due to the exogenous events such as meteor strikes, or massive volcanic eruptions. At other times they’re due to a build-up from the change of seasons. A common element is the amount of CO2 in the atmosphere. But the seasons continue regardless, though their nature can change. [Footnote – I know I’m simplifying these concepts.] https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661547270910-MFU21LSGYN7Y1RH2CDBU/Mackey+Glass.png Hypertext Book - Market Cycles vs. Macro Regimes - To illustrate the difference between a periodic and non-periodic cycle I’m showing a graph that has a sine wave with a period of 50 and the Mackey-Glass equation which has a non-periodic cycle of average length 50. The Mackey-Glass equation is a chaotic system used to model red blood cell production. This simulation has the same average period length as the sine wave but you can see that each individual cycle can be different than 50, sometimes significantly different. The market cycle works in much the same way. The stock market has an average length of four years (A result I published in my book “Chaos and Order in the Capital Markets”), but can vary significantly from cycle to cycle. https://www.edgarepeters.com/blog-2-2/constructing-the-indicators monthly 0.5 2023-10-09 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661362875454-EZLEGV8J3PYL04T2YI6G/cconstruction+photo.jpg Hypertext Book - Constructing Market Cycle and Macro Regime Indicators - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661367407501-X9KK5PS9KPWKWR8QFMEV/birds+flying.jpg Hypertext Book - Constructing Market Cycle and Macro Regime Indicators - Constructing market state indicators is much the same, though there is more uncertainty in them because, unlike the cocktails, we don’t know all of the ingredients for something like a recession. To use another analogy, it would be similar to the methodology ancient people would have used to predict the seasons. By “ancient” here I’m talking about before civilization when we roamed in tribes hunting and gathering. Back then we didn’t have calendars and definitely didn’t know that seasons were caused by the tilt of the Earth towards the sun. So instead we would look for signs that winter was coming. Things like leaves turning color, the days feeling colder, the sun being lower on the horizon, and birds flying south. Any one of these signs without the others wouldn’t mean anything. But as more and more of them built up, our ancestors would think winter was coming, so its time to prepare. The signs they used were actually leading indicators, and as more of them turned on the preponderance of the evidence would point to a seasonal change. While ancient people didn’t know the causality behind seasonal change they could observe the symptoms of such change and so tell one state from another. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661367734175-LAOE36E9U5KOMAKPSGB8/radar.jpg Hypertext Book - Constructing Market Cycle and Macro Regime Indicators - Analyzing each binary signal’s threshold is based upon a technique called ROC analysis. ROC stands for “Receiver Operating Characteristic” and was originally developed in World War 2 for radar analysis. Basically, its a way to determine whether you’re making a Type 1 or 2 error. By using many samples you can find at what level the indicator reaches maximum accuracy. As a freebee I can say that the threshold for the Markit PMI to predict an economic slow down is not 50 but 52. The Markit Purchasing Managers Index (PMI) is a survey of businesses on current business conditions. The answers to the survey are complied so that when the PMI is above 50 it means that more managers think that conditions are improving, and when its below 50 conditions are deteriorating. For this reason the interpretation of the PMI typically uses 50 as a threshold. But the ROC analysis showed that slowdowns in GDP were more accurately predicted when the PMI was below 52. This likely reflects the human tendency to be overly optimistic most of the time. So in my indicators when the Global PMI drops below 52 it means we’re heading into a manufacturing recession. Likewise the PMI has to rise to above 52 to signal recovery and renewed growth. So using ROC analysis we can determine the proper thresholds to construct binary signals. https://www.edgarepeters.com/blog-2-2/the-financial-instability-minsky-regime monthly 0.5 2023-10-09 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1667150622035-QPSJIPK75ZNTR1GPNAGF/gold+coins+spiraling+into+a+black+hole.png Hypertext Book - Financial Instability (“Minsky”) Regimes - “Stability leads to instability. The more stable things become and the longer things are stable, the more unstable they will be when the crisis hits.” - Hyman Minsky https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661434990826-O1RVFTSCR44WLTE927T5/minsky-moment.png Hypertext Book - Financial Instability (“Minsky”) Regimes - Academic research has shown that the financial instability cycle lasts from 8 to 20 years and is longer than the business or market cycle, which is 4 to 6 years. But when these cycles coincide, the resulting recessions tend to be longer and deeper than recessions caused by issues in the real economy or a stock market decline. The GFC, again, was a textbook example of this phenomena. So it would be useful to know when an approaching recession is tied to the financial system as opposed to the business or stock market cycle. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/79f36a22-62ca-4d69-b433-b2d281c26fb7/Minsky+cycle+2.png Hypertext Book - Financial Instability (“Minsky”) Regimes - Combining these two measures together creates four states: 1) Normal liquidity: leverage is low and market uncertainty is low 2) Normal leverage: leverage is high and market uncertainty is low 3) Excessive leverage: leverage is high and market uncertainty is high 4) Excessive liquidity: leverage is low and market uncertainty is high https://www.edgarepeters.com/blog-2-2/the-reflation-cycle monthly 0.5 2025-02-09 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1667151219959-SHXD83T583JDZM1DCFBK/bubbles+in+a+spiral+.png Hypertext Book - Short-term Reflation Expectation Cycles - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661435862146-9219MEG4VOVXWB8526CP/sticky+inflation+fred+graph.png Hypertext Book - Short-term Reflation Expectation Cycles - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.edgarepeters.com/blog-2-2/the-inflation-cycle monthly 0.5 2023-10-06 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1667151535850-JH60GUZT61BN0UONOOAU/arrows+going+up+in+a+diagonal.png Hypertext Book - Long-term Inflation Regimes - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661786975571-62AVZB2EJI0REZP11T64/velocity+of+money+fred.png Hypertext Book - Long-term Inflation Regimes - From the St Louis FRED website: “Velocity is a ratio of nominal GDP to a measure of the money supply (M1 or M2). It can be thought of as the rate of turnover in the money supply--that is, the number of times one dollar is used to purchase final goods and services included in GDP.” https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661802176268-PXXKEVYKLPIIGXZ0IH76/Inflation+regime+sig.png Hypertext Book - Long-term Inflation Regimes - The Inflation Regime Indicator from 1948 - June 2022. The “6 month forward CPI” is the headline CPI 6 months in the future. The IRI can be read as follows: <0.50 = Low, 0.50 = Moderate, 0.75 = High, and 1.00 = Very High. Plotting the IRI vs. 6 month ahead inflation shows how effectively the indicator anticipates changes in the inflation regime. Source: St. Louis Fed, FMCR Analytics https://www.edgarepeters.com/blog-2-2/blog-post-title-two-l8hwl monthly 0.5 2023-10-06 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1bcfb4b6-f3ac-4e69-9d1c-104c4297c71f/iceberg+in+the+style+of+rockwell+kent.png Hypertext Book - Market Uncertainty Cycles - “For uncertain matters there are no calculable probabilities whatsoever. We simply do not know.” - John Maynard Keynes, A Treatise on Probability 1921 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1661525784370-HXLKJOLRDASYOMQOVMN0/MUSI+spaghetti+graph.png Hypertext Book - Market Uncertainty Cycles - Resilient and Fragile States: 1988 - 2018 Source: MSCI, St Louis Fed, FMCR Analytics Risk and return over the two states for various asset classes. https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/272d124f-265d-46ef-a2f2-93a07db2ab27/MUSI+critical+2.png Hypertext Book - Market Uncertainty Cycles - The MUSI has five states. The first three relate to market uncertainty alone: A resilient state when fundamental risks are low, A transition state when there is a mixture, and A turbulent state when most risks are high. But there are two more states that link to the longer cycles of inflation levels and the financial instability caused by excessive leverage: A fragile state when market risks are high, and financial leverage is high but inflation levels are low, and A critical state where market risk, financial leverage and inflation levels are high. Inflation and financial instability risk play the same role that the “z” axis causes for the Lorenz Attractor or El Nino does for climatology. They shift the market cycle to different regimes. https://www.edgarepeters.com/home daily 1.0 2025-03-29 https://www.edgarepeters.com/publications daily 0.75 2026-03-27 https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1660331000338-7R6CZAFEMMYWPQ5GMM7G/Chaos+and+Order.jpg https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1660331125861-FEMT41061K7O5OV9W9V4/FMA.jpg https://images.squarespace-cdn.com/content/v1/62dd7afae82484207a37da2a/1660331256834-UQ9B6SM6WLCKJ66S3ZMM/Patterns+Dark.jpg https://www.edgarepeters.com/new-page-2 daily 0.75 2025-09-28 https://www.edgarepeters.com/start-here-copy-3 daily 0.75 2024-08-19 https://www.edgarepeters.com/store daily 0.75 2025-09-28