# Thesis on an Empirical Study of Elliot Wave Analysis

FX:EURUSD   Euro / U.S. Dollar
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Elliot Waves - A Market Aesthetic
An Emergent Feature of Equity Markets and Market Psychology

Developed by Ralph Nelson Elliot in the 1930s, the Elliot wave principle became a tool for technical analysis used to chart and forecast financial market cycles by identifying extremes in investor psychology and other factors. The Elliot wave principle is a concept built upon a foundation of Fibonacci ratios and market sentiment. Fibonacci ratios are a fundamental tool in most of today’s traders' technical analysis tool belt. The numbers derived from the Fibonacci sequence can be divided to create the mathematical product that is commonly referred to as the golden-ratio that plays a significant role in the emerging structures and patterns attributed to equities markets.

Why is this?

The volatility and chaos are observed and experienced by traders involved with the foreign exchange, and that chaos is a result of the trillions of dollars that is moved within the currency market. Those same trillions of dollars also generate structure within the system and is a concept that can be further illustrated by law of large numbers. The law of large numbers is central in understanding mathematical concepts such as probability theory and thermodynamics, connecting the natural world to the man-made world of financial markets within a gradient between two vectors from a prior to a posteriori. A priori is knowledge that is synthesized independent from experience. It is an abstract idealism studied within the domain metaphysics. The study of mathematics is a relevant example of a priori knowledge that being governed by axioms rooted in the study of logic removed from reality. A posteriori is experiential knowledge and is thus empirical.

What's up with the law of large numbers?

The concept of the law of large numbers can be summarized as such; an increased frequency of observable values over time should be equivalent to the expected value. We can expect the average over time to equivalent the an expected value. We can make a relational inference from the concept of expected value to the "fair-value" of an asset, such as a currency pair. This will be significant in order-flow analysis or other types of volume trading techniques. When a technical indicator, such as the fixed range volume profile , is applied to a chart, we generate a distribution curve of significant volumes from a selected range (sometimes we generate multiple distributions from a single range). This feature also generates a point-of-control, which is the most significantly traded price level, the expected value in our law of large numbers generated from our observable sample-size derived from our selected range. In essence, the market will shift in attempt to stabilize at equilibrium or move towards (regress) to the point-of-control (to the mean).

Volume (or market) profile is an x-axis indicator, meaning that it quantifies independent variables. Examples of independent variables in the foreign exchange market are as such; human behavior and economics and political events. The price of a currency pair is recorded and plotted on the y-axis. The resulting price is a dependent variable. This means that price is "dependent" or influenced by the independent variables mentioned from our x-axis. Trade volume is significant to quantify and observe due to traders executing trades, thus acting on the with dynamic forces of the a market that is being governed by the laws supply and demand (which is central to order-flow analysis and volume trading techniques).

Market liquidity is measurement of the speed at which price changes or the frequency at which a currency is pair is exchanged over time. The relationship between volume and liquidity is direct. The liquidity of the market also affects the depth of the market influencing price action. Price action analysis is a type of technical analysis that attempts to reveal market sentiment by analyzing "naked indicators" or candle-sticks (OHLC by period of time) and trends. X-axis forces are revealed by the formation of candlesticks making price action the basis of all technical analysis .

What does this have to do with thermodynamics? This is the domain of finance and economics, not science!

Thermodynamics is a branch of physics that attempts to answer how energy moves and achieves equilibrium within a system. We can borrow from the lexicon of thermodynamics and apply it to the market in our exhibition, EURUSD . The second law of thermodynamics describes, in summary, how states of matter and energy transition from order to disorder in a system (the delta value of entropy in a system). Entropy is the measurement of chaos in a system. In chemistry, we learn that entropy is a measurement of the energy potential generated by various chemical species in a system. New chemical species emerge when catalyzed by an event resulting in a rapid rate of entropy. Initially, this results in a system of disorder and over time moving to a system of order meeting energy equilibrium resulting in chemical species with new chemical bonds. Other ways to describe this event using our new mixed glossary of terminology borrowed from different domains of knowledge would be; the system had moved from a state of high (or low) entropy and met equilibrium, the average observable energy potential is at or near the expected value, or the energy potential within the system had regressed to the mean.

In the exhibition above ( EURUSD ), we ranged the fixed-range volume profile indicator on EURUSD to our mapped Elliot wave to provide empirical proof that Elliot waves are a natural phenomena of human emotion on equity markets. The point-of-control is the red-line projecting from the distribution curve and is the level at which most of the trading volume takes place. This is comparable to a support/resistance zones, a psychological trading concept. Our range has generated a single distribution curve from the volume profile indicator. The highlighted area is our value-area (70% distribution) and is the area of value with the most trading significance.

It is notable that wave ((ii)) (on the minute wave), price had retraced to the 0.5 fib level (although not a traditional fib ratio, it is acceptable within the guidelines of the Elliot wave principle). The fixed range volume profile indicator revealed a significant shift in supply that moved the pair into a retracement resulting in wave ((i)) before exhausting the sellers momentum to create wave ((ii)). The less opaque areas of the volume distribution are levels where we see a shift left on the supply curve (reduced supply of contracts around the point-of-control) resulting in the higher demand to drive EURUSD from wave ((ii)) to the long wave ((iii)). This less opaque area of volume distribution are where the price tends "run away” because of the lack of either supply or demand in the market that had resulted in the impulse wave ((iii)), which is the always the largest move in an Elliot wave structure. The consolidation of volume and price that is revealed by the volume profile indicator at wave ((ii)) is significant as it proves wave 3 is a result of exhausted trading “pressure.” It also is interesting to note that our point-of-control also sits atop wave (v) concluding an impulse drive in the minuette cycle, resulting in a complex wave ((iii)) pattern and thus providing further confirmation of a strong support/resistance level.

Conclusion

Much like how the natural world is in flux, so too are our financial markets. Emotional agents create conditions of volatility in the fx market. The laws of supply and demand move price in an ebb and flow across time in an attempt to find market equilibrium at the expected value, all while the lattice structures emerge composing the Elliot waves that provides structure and order to a seemingly orderless system. Fibonacci ratios are the “atomos” revealing price patterns and guidance for these waves to form, similar to how the recurring patterns found in nature reveal the Fibonacci sequence. A concept rooted in aesthetics, axiology, and market behavior, Elliot waves are a product of emergence.
Comment: I apologize for some of the spelling mistakes and redundancy. I became heavily invested in this idea and stayed up late writing this out. I thought I had thoroughly proof-read this article. lol
Comment: In the section describing how volume and supply-and-demand move price to create Elliot Waves, I had incorrectly stated that the retracement resulted in wave ((i)). The retracement should be attributed to wave ((ii)).
Comment: We can add confluence and confirmation using the COT report. The COT report indicates that as of March, we have entered a bull market with EU.