Algorithmic Dominant Extrema Tracking

In the fast-paced world of financial markets, identifying significant price movements, often referred to as swings, is crucial for traders and analysts. The accuracy and speed of detecting these swings directly impact trading strategies and decision-making. Traditional methods, while functional, can be computationally intensive, especially when dealing with large datasets. This is where algorithmic dominant extrema tracking comes into play, offering a more efficient and refined approach to pinpointing these critical market turning points. By focusing on only the most significant price points, we can dramatically reduce the computational load without sacrificing accuracy, leading to faster and more reliable swing detection.

The Core Idea: Significance Over Volume

The fundamental principle behind algorithmic dominant extrema tracking is the realization that not all price points within a lookback period are equally important for defining a valid swing. Think of it this way: when you're drawing a trend line or identifying a support/resistance level, you're not considering every single tick or bar. Instead, you're focusing on the peaks (local maxima) and troughs (local minima) that stand out. These are the dominant extrema. The insight here is that most bars in a given lookback window are simply noise – they don't represent a true reversal or a significant turning point. By filtering out these less important bars, we can drastically shrink the number of potential swing endpoints we need to analyze. Instead of evaluating every possible pair of bars within a lookback window, which can grow quadratically (O(lookback²)), we can focus on a much smaller set of dominant extrema, reducing the complexity to roughly O(dominant_extrema²). For instance, with a lookback of 50 bars, a brute-force approach might consider up to 2,500 pairs. However, by tracking only dominant extrema, this number could shrink to as few as 25-100 pairs, a massive improvement in efficiency.

Why Dominant Extrema Matter: The Structural Significance

The concept of dominant extrema is rooted in the very definition of a valid swing in technical analysis. A key rule, often found in documentation like Docs/Reference/valid_swings.md (Rule 2.1), states that for a swing to be valid, no bar between the swing's high and low can have a price that exceeds the swing's highest point (for a bullish swing) or falls below the swing's lowest point (for a bearish swing). This rule has a profound implication: the origin of a valid swing must be the absolute highest point (for a bull swing) or lowest point (for a bear swing) within its defined range. If a higher high or a lower low occurs after the supposed origin but before the pivot point of that swing, the entire swing is invalidated. This is where algorithmic dominant extrema tracking shines. It directly addresses this rule by focusing our analysis only on bars that have the potential to be a valid swing origin or pivot. A bar whose high is easily surpassed by a nearby bar can never serve as the origin of a valid bullish swing. Similarly, a bar whose low is easily undercut cannot be the origin of a valid bearish swing. By pre-emptively filtering out these non-dominant bars, we ensure that our subsequent swing formation logic only considers truly significant price points, making the entire process more robust and computationally efficient. This isn't just a minor optimization; it's a fundamental shift in how we approach swing detection, moving from a comprehensive, but potentially slow, scan to a targeted, high-impact analysis.

Implementing Dominant Extrema Tracking: A Step-by-Step Guide

Implementing algorithmic dominant extrema tracking involves several key steps, focusing on identifying, tracking, and confirming these significant price points. We'll break this down into defining what constitutes a dominant extremum, how to track potential candidates, and how to update our tracking as new market data comes in.

Step 1: Defining Dominant Extrema

At its core, a dominant high is a bar whose high price is not exceeded by any bar within a specified dominance_window. Furthermore, this high must not have been undercut or surpassed by a subsequent bar since it occurred. Conversely, a dominant low is a bar whose low price is not surpassed by any bar within the dominance_window, and this low must not have been exceeded by a subsequent bar since it occurred. The dominance_window is a crucial parameter, acting as a buffer to confirm that a high or low is indeed locally significant. A recommended starting value for dominance_window is 5 bars. This means we wait for 5 bars after a potential extremum to pass before confirming its dominance. This small window is usually sufficient to filter out minor fluctuations while still keeping the computational overhead low.

Step 2: Tracking Pending and Confirmed Extrema

To manage these dominant extrema efficiently, we need a structured way to track them. Instead of flat lists of all historical candidates, we'll use a state object that distinguishes between pending and confirmed extrema. This state typically includes:

• pending_highs: A list of potential highs that have occurred recently but haven't yet passed the dominance_window. Each entry would be a tuple of (index, price).
• pending_lows: Similar to pending_highs, but for low prices.
• dominant_highs: A list of highs that have successfully passed the dominance_window and are confirmed as dominant. These are the primary candidates for swing origins.
• dominant_lows: Confirmed dominant low prices.
• pending_high_max: To speed up pruning, we can track the highest price seen within the current pending_highs window.
• pending_low_min: Similarly, the lowest price within the pending_lows window.

This structured approach allows for quick checks and efficient updates as new bars arrive.

Step 3: Updating Candidate Tracking

As each new bar arrives, we need to update our tracking lists. This involves several logical checks:

1. Invalidate Pending Extrema: For highs, we check if the new bar.high exceeds any pending_highs. If it does, those pending highs are no longer dominant and are removed. The same logic applies symmetrically for lows.
2. Prune Confirmed Extrema: We also need to ensure that our dominant_highs and dominant_lows lists stay relevant to the current lookback period. Any confirmed extrema that fall outside this lookback window are removed.
3. Add Current Bar: The current bar's high and low are added to their respective pending_highs and pending_lows lists.
4. Promote Pending to Dominant: This is where the dominance_window comes into play. We calculate a cutoff index (current bar index minus dominance_window). Any pending extrema with an index less than or equal to this cutoff have successfully survived the dominance period. They are then moved from the pending lists to the dominant lists. The remaining pending extrema stay in their lists, awaiting further confirmation or potential invalidation.

This continuous update process ensures that our lists of dominant_highs and dominant_lows always reflect the most structurally significant price points observed within the relevant lookback period.

Step 4: Refining Swing Formation Logic

With the dominant_highs and dominant_lows lists now populated with only the most significant extrema, the logic for forming swings can be significantly simplified. The core swing formation algorithm remains similar, but instead of iterating through all historical candidate highs and lows, it now iterates through the much smaller lists of dominant_highs and dominant_lows. For instance, when trying to form a bullish swing (which requires an origin high followed by a defended pivot low), the algorithm would use self.state.dominant_highs for potential origins and self.state.dominant_lows for potential pivots. This drastically reduces the number of comparisons needed in the swing formation step, directly contributing to performance gains.

Step 5: Configuration Enhancements

To make this new approach flexible and adaptable, the configuration needs to be updated. A new field, dominance_window, should be added to the swing configuration. This allows users to easily adjust the sensitivity of the dominant extrema detection. A default value, such as 5, provides a good starting point, but the ability to tune this parameter is essential for different market conditions or trading styles. Other configuration parameters like lookback_bars remain crucial for defining the overall historical context.

Step 6: Early Termination per Origin (Bonus Optimization)

An additional optimization, often referred to as