Poisson Projection of Price Levels

前天

### **Poisson Projection of Price Levels**

**Overview:**
The *Poisson Projection of Price Levels* is a cutting-edge technical indicator designed to identify and visualize potential support and resistance levels based on historical price interactions. By leveraging the Poisson distribution, this tool dynamically adjusts the significance of each price level's past "touches" to project future interactions with varying degrees of probability. This probabilistic approach offers traders a nuanced view of where price levels may hold or react in upcoming bars, enhancing both analysis and trading strategies.

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**🔍 **Math & Methodology**

1. **Strata Levels:**
- **Definition:** Strata are horizontal lines spaced evenly around the current closing price.
- **Calculation:**
\[
\text{Strata Level}_i = \text{Close} - \frac{\text{Increment} \times \text{Strata Count}}{2} + i \times \text{Increment}
\]
where \(i\) ranges from 0 to \(\text{Strata Count} - 1\).

2. **Forecast Iterations:**
- **Structure:** The indicator projects five forecast iterations into the future, each spaced by a Fibonacci sequence of bars: 2, 3, 5, 8, and 13 bars ahead. This spacing is inspired by the Fibonacci sequence, which is prevalent in financial market analysis for identifying key levels.
- **Purpose:** Each iteration represents a distinct forecast point where the price may interact with the strata, allowing for a multi-step projection of potential price levels.

3. **Touch Counting:**
- **Definition:** A "touch" occurs when the closing price of a bar is within half the increment of a stratum level.
- **Process:** For each stratum and each forecast iteration, the indicator counts the number of touches within a specified lookback window (e.g., 80 bars), offset by the forecasted position. This ensures that each iteration's touch count is independent and contextually relevant to its forecast horizon.
- **Adjustment:** Each forecast iteration analyzes a unique segment of the lookback window, offset by its forecasted position to ensure independent probability calculations.

4. **Poisson Probability Calculation:**
- **Formula:**
\[
\lambda = \frac{\text{Number of Touches}}{\text{Lookback Window}}
\]
\[
p(k=1) = \lambda \times e^{-\lambda}
\]
- **Interpretation:** \(p(k=1)\) represents the probability of exactly one touch occurring within the lookback window for each stratum and iteration.
- **Application:** This probability is used to determine the transparency of each stratum line, where higher probabilities result in more opaque (less transparent) lines, indicating stronger historical significance.

5. **Transparency Mapping:**
- **Calculation:**
\[
\text{Transparency} = \min(100, \max(0, 100 - \left(\frac{p}{\text{Threshold}}\right) \times 100))
\]
- **Purpose:** Maps the Poisson probability to a visual transparency level, enhancing the readability of significant strata levels.
- **Outcome:** Strata with higher probabilities (more historical touches) appear more opaque, while those with lower probabilities appear fainter.

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**📊 **Comparability to Standard Techniques**

1. **Support and Resistance Levels:**
- **Traditional Approach:** Traders identify support and resistance based on historical price reversals, pivot points, or psychological price levels.
- **Poisson Projection:** Automates and quantifies this process by statistically analyzing the frequency of price interactions with specific levels, providing a probabilistic measure of significance.

2. **Statistical Modeling:**
- **Standard Models:** Techniques like Moving Averages, Bollinger Bands, or Fibonacci Retracements offer dynamic and rule-based levels but lack direct probabilistic interpretation.
- **Poisson Projection:** Introduces a discrete event probability framework, offering a unique blend of statistical rigor and visual clarity that complements traditional indicators.

3. **Event-Based Analysis:**
- **Financial Industry Practices:** Event studies and high-frequency trading models often use Poisson processes to model order arrivals or price jumps.
- **Indicator Application:** While not identical, the use of Poisson probabilities in this indicator draws inspiration from event-based modeling, applying it to the context of price level interactions.

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**💡 **Strengths & Advantages**

1. **Innovative Visualization:**
- Combines statistical probability with traditional support/resistance visualization, offering a fresh perspective on price level significance.

2. **Dynamic Adaptability:**
- Parameters like strata increment, lookback window, and probability threshold are user-defined, allowing customization across different markets and timeframes.

3. **Independent Probability Calculations:**
- Each forecast iteration calculates its own Poisson probability, ensuring that projections are contextually relevant and independent of other iterations.

4. **Clear Visual Cues:**
- Transparency-based coloring intuitively highlights significant price levels, making it easier for traders to identify key areas of interest at a glance.

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**⚠️ **Limitations & Considerations**

1. **Poisson Assumptions:**
- Assumes that touches occur independently and at a constant average rate (\(\lambda\)), which may not always align with market realities characterized by trends and volatility clustering.

2. **Computational Intensity:**
- Managing multiple iterations and strata can be resource-intensive, potentially affecting performance on lower-powered devices or with very high lookback windows.

3. **Interpretation Complexity:**
- While transparency offers visual clarity, understanding the underlying probability calculations requires a basic grasp of Poisson statistics, which may be a barrier for some traders.

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**📢 **How to Use It**

1. **Add to TradingView:**
- Open TradingView and navigate to the Pine Script Editor.
- Paste the script above and click **Add to Chart**.

2. **Configure Inputs:**
- **Strata Increment:** Set the desired price step between strata (e.g., `0.1` for 10 cents).
- **Lookback Window:** Define how many past bars to consider for calculating Poisson probabilities (e.g., `80`).
- **Probability Transparency Threshold (%):** Set the threshold percentage to map probabilities to line transparency (e.g., `25%`).

3. **Understand the Forecast Iterations:**
- The indicator projects five forecast points into the future at bar spacings of 2, 3, 5, 8, and 13 bars ahead.
- Each iteration independently calculates its Poisson probability based on the touch counts within its specific lookback window offset by its forecasted position.

4. **Interpret the Visualization:**
- **Opaque Lines:** Indicate higher Poisson probabilities, suggesting historically significant price levels that are more likely to interact again.
- **Fainter Lines:** Represent lower probabilities, indicating less historically significant levels that may be less likely to interact.
- **Forecast Spacing:** The spacing of 2, 3, 5, 8, and 13 bars ahead aligns with Fibonacci principles, offering a natural progression in forecast horizons.

5. **Apply to Trading Strategies:**
- **Support/Resistance Identification:** Use the opaque lines as potential support and resistance levels for placing trades.
- **Entry and Exit Points:** Anticipate price interactions at forecasted levels to plan strategic entries and exits.
- **Risk Management:** Utilize the transparency mapping to determine where to place stop-loss and take-profit orders based on the probability of price interactions.

6. **Customize as Needed:**
- Adjust the **Strata Increment** to fit different price ranges or volatility levels.
- Modify the **Lookback Window** to capture more or fewer historical touches, adapting to different timeframes or market conditions.
- Tweak the **Probability Transparency Threshold** to control the sensitivity of transparency mapping to Poisson probabilities.

**📈 **Practical Applications**

1. **Identifying Key Levels:**
- Quickly visualize which price levels have historically had significant interactions, aiding in the identification of potential support and resistance zones.

2. **Forecasting Price Reactions:**
- Use the forecast iterations to anticipate where price may interact in the near future, assisting in planning entry and exit points.

3. **Risk Management:**
- Determine areas of high probability for price reversals or consolidations, enabling better placement of stop-loss and take-profit orders.

4. **Market Analysis:**
- Assess the strength of market levels over different forecast horizons, providing a multi-layered understanding of market structure.

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**🔗 **Conclusion**

The *Poisson Projection of Price Levels* bridges the gap between statistical modeling and traditional technical analysis, offering traders a sophisticated tool to quantify and visualize the significance of price levels. By integrating Poisson probabilities with dynamic transparency mapping, this indicator provides a unique and insightful perspective on potential support and resistance zones, enhancing both analysis and trading strategies.

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**📞 **Contact:**
For support or inquiries, please contact me on TradingView!

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**📢 **Join the Conversation!**
Have questions, feedback, or suggestions for further enhancements? Feel free to comment below or reach out directly. Your input helps refine and evolve this tool to better serve the trading community.

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**Happy Trading!** 🚀

前天

版本注释

Smaller price increments for stratification now allowed. Optimized for sub minute charts for some low priced assets such as cryptocurrencies or dying stocks.