ExtremeHurst Predictor

APPS CS : EHURST

Aftershocks are also log‐periodic, but are expanding, which means the highs and lows are getting farther
apart logarithmically over time. The Video to the right are  simulated log-periodic oscillations culminating in a critical reversal point and then expanding away from the critical point (Top Extension)

Magnitude Variance
Wave Length Variance
Phase Shifting
Falloff Response Variance

Second, the build up to a critical point resembles the power law function C1*(1-t/tc)x , where C1 is a constant, x is a negative power, t is time, and tc is the time of the critical point. Thirdly, there is a log-periodic ripple in price that converges to the critical point that has the form: 1+C2*cos[ p*ln(1- t/tc)+q ] , where ln(x) is the natural log function, cos(x) is the cosine function, and C2, p, and q are real constants[30].

Another way to think of these signals is to envision a mass on a spring. When the spring is compressed, the system has high potential energy. When the mass is released, it will move very fast away from its starting position. In fact, it will then move too far. An extension occurs as the spring reaches its full extent, just before it settles back

What is ExtremeHurst?

ExtremeHurst is a quantitative detector of extreme investor behavior that signals the beginning or end of a trend. Strong trend‐persistent stock price movements are evidence of positive feedback (i.e.,investors buying because the price is rising, driving prices higher), while extremes of mean reversion are evidence of negative feedback. Extremes of both trend persistency and mean reversion are quantified via multiple measurements of the Hurst exponent. Parallax found that Hurst extremes coupled with other characteristics, signal the beginning or end of market trends. ExtremeHurst signals are fully characterized by the presence of discrete scale invariance, accelerating price, log‐periodic cycles, and volume anomalies. This App allows the user to search global markets for signals on intraday, daily, weekly, monthly, and quarterly time scales. Signals have been found to persist for up to 20 bars.

ExtremeHurst exploits the science of non‐linear dynamics to identify unique and predictive signals occurring in freely trading auction markets. There are two types of ExtremeHurst signals that we call “Extensions” and “Compressions”. These correspond to the extreme high and low ends of the Hurst exponent distribution.

The Hurst exponent, as applied to a financial series, represents the degree of randomness which is present. Deviations from random take the form of mean‐reversion or trend persistency. The picture below shows five time series with different Hurst exponents. The topmost example is the most mean‐reverting, while the bottom example shows the most trend persistency. The middle one is random.

Research History

This section covers the basic science and the empirical results from our ExtremeHurst™ market predictor model. Our research started in the late 80’s with the observation that market series appeared to have no unique trend. An uptrend on a 5 minute chart might be embedded in a daily scale downtrend, and a monthly scale up trend, etc. It also made intuitive sense that no unique trend exists. After all, if it did, then all investors would quickly exploit it for profit.

So following this line of thought, we wondered what would happen next if a financial series simultaneously showed a measurably strong trend on at least two adjacent time scales, or even three. This is a deceptively simple question, but how is trend measured? How much trend is a strong trend? Are there preferred time scales? How much data is needed to evaluate trend? The answers to these questions led eventually to the discovery that elements of chaos theory, namely self-organized criticality [13, 30] and discrete scale invariance [25-27, 30] (discovered independently and named by Didier Sornette), have a statistically significant predictive power in financial markets and elsewhere. Here are the highlights of the journey.

Most scientists and engineers graduating in the 80’s or earlier were trained that experimental data usually approximated some smooth function, but with a bit of random measurement error. To the untrained eye, stock price data looks very similar to a smoothly trending signal covered up by a large amount of random noise. Even the price return distribution resembles a normal distribution, which implies a random process. The standard engineering approach in cases like this would be to fit a regression curve to the market series and write off the remainder to random noise [1]. Once a smooth curve
was found that fit prices well enough, one would just find the slope (“trend”) at each point. The trend would be unique by definition, and its direction would dictate the trade direction.

Figure . Typical regression curve fitted to data with the remainder attributed to random sources

If this sounds too simple to be true, you have graduated to the rest of the story. Chaos theory covers the dynamics of feedback systems [3, 8, 12, 18, 22, 30, 31]. Generally, feedback means that the outputs of the system are fed back into the system as new inputs to produce more outputs….and then this process continues until the loop is broken. Feedback can be negative, like in the case of a thermostat, or positive, as seen by placing a microphone near a speaker. In the financial markets we can imagine that price movement, news, or possibly influential people produce investment bias “output” that is fed into the brains of the investor community, who then produce new outputs in the form of buy and sell decisions. If this bias is positive, buying occurs, which leads to higher prices and more positive bias, etc. Feedback systems exhibit certain characteristics, which strangely enough, seem to match the kinds of phenomena that market technical analysts have attributed to markets over the last 100 years. Self-similarity is the primary example.

Financial series appear to have the same “look” on many different time scales. This is called self-similarity, and it happens to be one of the best ways to confirm that a series is governed by the rules of chaos theory. Put another way, the market is what Mandelbrot [14] called a “fractal.” Not quite like a fern or a snowflake, but more of a statistical fractal like a shoreline. We chose a fractal function developed by Weierstrass to model a market series [8]. Weierstrass functions are continuous, meaning you can draw one without lifting your pencil, but they have no unique slope. They look like a cycle inside a cycle inside a cycle as shown in the next figure. Market technicians call this effect the “Elliot Wave”, but self-similarity has a much deeper theoretical meaning firmly based in non-linear dynamics.

ExtremeHurst Extensions

Extensions correspond to extreme levels of trend persistency on multiple scales, and mark the end of
trend persistent periods, either at market tops or bottoms. The picture below shows multiple Hurst
exponent measurements for a particular security at different scales. The shortest scales are on the
bottom. Red represents persistent down trends. Green represents persistent up trends. Gray shows
random price movement, and blue represents mean‐reverting exponents. Note the column of red at
the price low
Many factors influence investors, but we choose to focus on the extremes of competitive or cooperative behavior from a macro perspective. Feedback is at the heart of why ExtremeHurst works. Investors
sometimes behave as herds, selling because the price is dropping, or buying because it’s going up.
Panics and manias are large scale examples of this. However, when most investors agree that a stock is
going up or down, they’ve probably already acted on their belief, and the buying or selling dries up,
leading to a reversal.

Elements of Log Periodicity

ExtremeHurst Compressions

There was another key timing factor in addition to the parabolic price move which we literally stumbled upon while trying to limit our Hurst sampling. Cycles were present during these parabolic moves, and by exploiting them, we were better able to time the critical point. The next section discusses log periodic cycles and the science that ties it all together.

Extremes of investor behavior are most evident in large scale market manias or crashes, but like earthquakes, significantly more low magnitude events occur than large ones. It is our contention that markets set themselves up in critical states through feedback, like earthquakes, and then we see tremor-like activity of all sizes and scales at both highs and lows. This area of scientific research is called “Self-Organized Criticality” or SOC for short. Bak, Tang, and Weisenfield (BTW) [36] first introduced SOC in 1987 by studying the occurrences of avalanches in sand pile models. It was their contention that large systems with many constituent parts, organize themselves into states that resemble systems in equilibrium at critical points.

In the case of the markets, investors are influenced by news, price changes, and other investors within their local social network. This influence conditions their willingness to buy or sell, which in turn affects price and influences others, and so on. One of the methods used to understand the dynamics of large critical systems is called the Renormalization Group Method [10, 13, 27, 30] this method uses scaling to make sense of complex systems. Temperature is an example of this idea. We wouldn’t think of tracking each air molecule to calculate heat (except maybe in a physics lab), so we characterize the behavior of a large group of molecules instead by their temperature. We have applied this same method to learn some basic principles about markets: First, it takes very few net buyers or sellers to trigger a buying or selling trend, or end one.

While in the log time domain it becomes a sine wave:

Compressions correspond to extreme levels of mean‐reversion, or investor competition, on multiple scales. These signals mark the beginning of trends by finding when the vigorous competition between supply and demand has reached a critical point. Price is expected to move very rapidly away from its current price following a compression.

How do I use ExtremeHurst?

The ExtremeHurst signals work on all freely traded securities and on all time scales, provided sufficient liquidity is present. For a “crowd effect” to occur, a crowd must be present. The predictive edge lasts 15‐20 price “bars”, so for monthly scale data, this means the effect might continue for as long as 20 months.The Extension signals predict retracement or sideways periods, so redeployment of capital may be the best strategic move. Aggressive speculators like to play the log‐periodic cycles, so we have included the expected top and bottom timing marks on the charts and in the signal file.

 

Extensions

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Compressions


Compressions mark the start of new trends, but we never know the direction, so a straddle or triggered
L/S entry is required.

Options Trading

Signals have at least four critical uses:

1. Trade positioning

2. Profit taking.

3. Identifying transitions from a trending to a sideways market or from a sideways to a trending market.

4. When the crowd runs a security too far up or down, prices can deviate significantly from a reasonable valuation and diminish portfolio performance


. Having an idea about when these effects are occurring can be very valuable.
Signals are ranked from 1 to 100 depending on how closely they correspond to the ideal signal

An ideal signal exhibits four characteristics:
1. A price acceleration that deviates significantly from normal Gaussian expectations
2. Extreme Hurst Exponent measurements on multiple scales
3. Log‐periodic price ripples which converge to the signal date
4. Unique price and volume sequencing
We combine factors using a pre‐trained neural net to produce our final signal rank
We have created the ExtremeHurst App on Bloomberg to enable users to search world markets for
these predictive signals on intraday, daily, weekly, monthly, and even quarterly time scales.

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Our clients range from FTSE 300 companies, to large charitable organisations and some small local businesses who are striving to expand. Most of our clients use our Data Analysis service to inform their strategic decision making and their targets for the immediate, mid-term and long-term future.

The data sources that we use for this type of analysis include customer enquiry data, sales figures, costs, market data and customer feedback.

Bloomberg: The Power of < GO >

Our clients range from FTSE 300 companies, to large charitable organisations and some small local businesses who are striving to expand. Most of our clients use our Data Analysis service to inform their strategic decision making and their targets for the immediate, mid-term and long-term future.

The data sources that we use for this type of analysis include customer enquiry data, sales figures, costs, market data and customer feedback.

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