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指標和策略

Z-Score Bands + SignalsZ-Score Statistical Market Analyzer A multi-dimensional market structure indicator based on standardized deviation & regime logic English Description Concept This indicator builds a statistical model of price behaviour by converting every candle’s movement into a Z-score — how many standard deviations each close is away from its moving average. It visualizes the normal distribution structure of returns and provides adaptive entry signals for both Mean Reversion and Breakout regimes. Rather than predicting price direction, it measures statistical displacement from equilibrium and dynamically adjusts the decision logic according to the market’s volatility regime. ⚙️ Main Components Z-Score Bands (±1σ, ±2σ, ±3σ) – The core structure visualizes volatility boundaries based on rolling mean and standard deviation. – Price outside ±2σ often indicates statistical extremes. Dual Signal Systems Mean Reversion (MRL / MRS): when price (or return z-score) crosses back inside ±2σ bands. Breakout (BOL / BOS): when price continues to expand beyond ±2σ. Volatility Regime Classification The indicator detects whether the market is currently in a low-vol or high-vol regime using percentile statistics of σ. Low vol → Mean Reversion preferred High vol → Breakout preferred 🧠 Adaptive Switches A. Freeze MA/σ - Use previous-bar stats to avoid repainting and lag. B. Confirm on Close - Only generate signals once the base-timeframe bar closes (eliminates look-ahead bias). C. Return-based Signal - Use log-return Z-score instead of price deviation — normalizes volatility across assets. D. Outlier Filter - Exclude bars with abnormal single-bar returns (e.g., >20%). Reduces false spikes. E. Regime Gating - Automatically switch between Mean Reversion and Breakout logic depending on volatility percentile. Each module can be toggled individually to test different statistical behaviours or tailor to a specific market condition. 📊 Interpretation When the histogram of returns approximates a normal distribution, mean-reversion logic is often more effective. When price persistently drifts beyond ±2σ or ±3σ, the distribution becomes leptokurtic (fat-tailed) — a breakout structure dominates. Hence, this tool can help you: Identify whether an asset behaves more “Gaussian” or “fat-tailed”; Select the correct trading regime (MR or BO); Quantitatively measure market tension and volatility clusters. 🧩 Recommended Use Works on any timeframe and any asset. Best used on liquid instruments (e.g., XAU/USD, indices, major FX pairs). Combine with volume, sentiment or structural filters to confirm signals. For strategy automation, pair with the companion script: 🧠 “Z-Score Strategy • Multi-Source Confirm (MRL/MRS/BOL/BOS)”. ⚠️ Disclaimer This script is designed for educational and research purposes. Statistical deviation ≠ directional prediction — use with sound risk management. Past distribution patterns may shift under new volatility regimes. ================================================================================== 中文说明（简体） 概念简介 该指标基于价格的统计分布原理，将每根 K 线的波动转化为标准化的 Z-Score（标准差偏离值），用于刻画市场处于均衡或偏离状态。 它同时支持 均值回归（Mean Reversion） 与 突破延展（Breakout） 两种逻辑，并可根据市场波动结构自动切换策略模式。 ⚙️ 主要功能模块 Z-Score 通道（±1σ / ±2σ / ±3σ） 用滚动均值与标准差动态绘制的统计波动带，价格超出 ±2σ 区域通常意味着极端偏离。 双信号系统 MRL / MRS（均值回归多空）：价格重新回到 ±2σ 以内时触发。 BOL / BOS（突破延展多空）：价格持续运行在 ±2σ 之外时触发。 波动率分层 自动识别市场处于高波动还是低波动区间： 低波动期 → 适合均值回归逻辑； 高波动期 → 适合突破趋势逻辑。 🧠 A–E 模块说明 A. 固定统计参数：使用上一根 K 线的均值和标准差，防止重绘。 B. 收盘确认信号：仅在当前时间框架收盘后生成信号，避免前视偏差。 C. 收益率信号模式：采用对数收益率的 Z-Score，更具普适性。 D. 异常波过滤：忽略单根极端波动（如 >20%）的噪声信号。 E. 波动率调节逻辑：根据市场处于高/低波动区间，自动切换 MRL/MRS 或 BOL/BOS。 📊 应用解读 如果收益率分布接近正态分布 → 市场倾向震荡，MRL/MRS 效果较佳； 若价格频繁偏离 ±2σ 或 ±3σ → 市场呈现“肥尾”分布，趋势延展占主导。 因此，该指标的核心目标是： 识别当前市场的统计结构类型； 根据波动特征自动切换交易逻辑； 提供结构化、可量化的市场状态刻画。 💡 使用建议 适用于所有时间框架与金融品种。 建议结合成交量或结构性指标过滤。 若用于策略回测，可搭配同名 “Z-Score Strategy • Multi-Source Confirm” 策略脚本。 ⚠️ 免责声明 本指标仅用于研究与教学，不构成任何投资建议。 统计偏离 ≠ 趋势预测，实际市场行为可能在不同波动结构下改变。
Pine Script®指標
由Xavante提供
True Average PriceTrue Average Price Overview The indicator plots a single line representing the cumulative average closing price of any symbol you choose. It lets you project a long-term mean onto your active chart, which is useful when your favourite symbol offers limited history but you still want context from an index or data-rich feed. How It Works The script retrieves all available historical bars from the selected symbol, sums their closes, counts the bars, and divides the totals to compute the lifetime average. That value is projected onto the chart you are viewing so you can compare current price action to the broader historical mean. Inputs Use Symbol : Toggle on to select an alternate symbol; leave off to default to the current chart. Symbol : Pick the data source used for the average when the toggle is enabled. Line Color : Choose the display color of the average line. Line Width : Adjust the thickness of the plotted line. Usage Tips Apply the indicator to exchanges with shallow history while sourcing the average from a complete index (e.g., INDEX:BTCUSD for crypto pairs). Experiment with different symbols to understand how alternative data feeds influence the baseline level. Disclaimer This indicator is designed as a technical analysis tool and should be used in conjunction with other forms of analysis and proper risk management. Past performance does not guarantee future results, and traders should thoroughly test any strategy before implementing it with real capital.
Pine Script®指標
由dchunt-stack提供
Price Action Brooks ProPrice Action Brooks Pro (PABP) - Professional Trading Indicator ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📊 OVERVIEW Price Action Brooks Pro (PABP) is a professional-grade TradingView indicator developed based on Al Brooks' Price Action trading methodology. It integrates decades of Al Brooks' trading experience and price action analysis techniques into a comprehensive technical analysis tool, helping traders accurately interpret market structure and identify trading opportunities. • Applicable Markets: Stocks, Futures, Forex, Cryptocurrencies • Timeframes: 1-minute to Daily (5-minute chart recommended) • Theoretical Foundation: Al Brooks Price Action Trading Method ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎯 CORE FEATURES ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1️⃣ INTELLIGENT GAP DETECTION SYSTEM Automatically identifies and marks three critical types of gaps in the market. TRADITIONAL GAP • Detects complete price gaps between bars • Upward gap: Current bar's low > Previous bar's high • Downward gap: Current bar's high < Previous bar's low • Hollow border design - doesn't obscure price action • Color coding: Upward gaps (light green), Downward gaps (light pink) • Adjustable border: 1-5 pixel width options TAIL GAP • Detects price gaps between bar wicks/shadows • Analyzes across 3 bars for precision • Identifies hidden market structure BODY GAP • Focuses only on gaps between bar bodies (open/close) • Filters out wick noise • Disabled by default, enable as needed Trading Significance: • Gaps signal strong momentum • Gap fills provide trading opportunities • Consecutive gaps indicate trend continuation ✓ Independent alert system for all gap types ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 2️⃣ RTH BAR COUNT (Trading Session Counter) Intelligent counting system designed for US stock intraday trading. FEATURES • RTH Only Display: Regular Trading Hours (09:30-15:00 EST) • 5-Minute Chart Optimized: Displays every 3 bars (15-minute intervals) • Daily Auto-Reset: Counting starts from 1 each trading day SMART COLOR CODING • 🔴 Red (Bars 18 & 48): Critical turning moments (1.5h & 4h) • 🔵 Sky Blue (Multiples of 12): Hourly markers (12, 24, 36...) • 🟢 Light Green (Bar 6): Half-hour marker (30 minutes) • ⚫ Gray (Others): Regular 15-minute interval markers Al Brooks Time Theory: • Bar 18 (90 min): First 90 minutes determine daily trend • Bar 48 (4 hours): Important afternoon turning point • Hourly markers: Track institutional trading rhythm ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 3️⃣ FOUR-LINE EMA SYSTEM Professional-grade configurable moving average system. DEFAULT CONFIGURATION • EMA 20: Short-term trend (Al Brooks' most important MA) • EMA 50: Medium-short term reference • EMA 100: Medium-long term confirmation • EMA 200: Long-term trend and bull/bear dividing line FLEXIBLE CUSTOMIZATION Each EMA can be independently configured: • On/Off toggle • Data source selection (close/high/low/open, etc.) • Custom period length • Offset adjustment • Color and transparency COLOR SCHEME • EMA 20: Dark brown, opaque (most important) • EMA 50/100/200: Blue-purple gradient, 70% transparent TRADING APPLICATIONS • Bullish Alignment: Price > 20 > 50 > 100 > 200 • Bearish Alignment: 200 > 100 > 50 > 20 > Price • EMA Confluence: All within <1% = major move precursor Al Brooks Quote: "The EMA 20 is the most important moving average. Almost all trading decisions should reference it." ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 4️⃣ PREVIOUS VALUES (Key Prior Price Levels) Automatically marks important price levels that often act as support/resistance. THREE INDEPENDENT CONFIGURATIONS Each group configurable for: • Timeframe (1D/60min/15min, etc.) • Price source (close/high/low/open/CurrentOpen, etc.) • Line style and color • Display duration (Today/TimeFrame/All) SMART OPEN PRICE LABELS ⭐ • Auto-displays "Open" label when CurrentOpen selected • Label color matches line color • Customizable label size TYPICAL SETUP • 1st Line: Previous close (Support/Resistance) • 2nd Line: Previous high (Breakout target) • 3rd Line: Previous low (Support level) Al Brooks Magnet Price Theory: • Previous open: Price frequently tests opening price • Previous high/low: Strongest support/resistance • Breakout confirmation: Breaking prior levels = trend continuation ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 5️⃣ INSIDE & OUTSIDE BAR PATTERN RECOGNITION Automatically detects core candlestick patterns from Al Brooks' theory. ii PATTERN (Consecutive Inside Bars) • Current bar contained within previous bar • Two or more consecutive • Labels: ii, iii, iiii (auto-accumulates) • High-probability breakout setup • Stop loss: Outside both bars Trading Significance: "Inside bars are one of the most reliable breakout setups, especially three or more consecutive inside bars." - Al Brooks OO PATTERN (Consecutive Outside Bars) • Current bar engulfs previous bar • Two or more consecutive • Labels: oo, ooo (auto-accumulates) • Indicates indecision or volatility increase ioi PATTERN (Inside-Outside-Inside) • Three-bar combination: Inside → Outside → Inside • Auto-detected and labeled • Tug-of-war pattern • Breakout direction often very strong SMART LABEL SYSTEM • Auto-accumulation counting • Dynamic label updates • Customizable size and color • Positioned above bars ✓ Independent alerts for all patterns ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 💡 USE CASES INTRADAY TRADING ✓ Bar Count (timing rhythm) ✓ Traditional Gap (strong signals) ✓ EMA 20 + 50 (quick trend) ✓ ii/ioi Patterns (breakout points) SWING TRADING ✓ Previous Values (key levels) ✓ EMA 20 + 50 + 100 (trend analysis) ✓ Gaps (trend confirmation) ✓ iii Patterns (entry timing) TREND FOLLOWING ✓ All four EMAs (alignment analysis) ✓ Gaps (continuation signals) ✓ Previous Values (targets) BREAKOUT TRADING ✓ iii Pattern (high-reliability setup) ✓ Previous Values (targets) ✓ EMA 20 (trend direction) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎨 DESIGN FEATURES PROFESSIONAL COLOR SCHEME • Gaps: Hollow borders + light colors • Bar Count: Smart multi-color coding • EMAs: Gradient colors + transparency hierarchy • Previous Values: Customizable + smart labels CLEAR VISUAL HIERARCHY • Important elements: Opaque (EMA 20, bar count) • Reference elements: Semi-transparent (other EMAs, gaps) • Hollow design: Doesn't obscure price action USER-FRIENDLY INTERFACE • Clear functional grouping • Inline layout saves space • All colors and sizes customizable ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 AL BROOKS THEORY CORE READING PRICE ACTION "Don't try to predict the market, read what the market is telling you." PABP converts core concepts into visual tools: • Trend Assessment: EMA system • Time Rhythm: Bar Count • Market Structure: Gap analysis • Trade Setups: Inside/Outside Bars • Support/Resistance: Previous Values PROBABILITY THINKING • ii pattern: Medium probability • iii pattern: High probability • iii + EMA 20 support: Very high probability ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ ⚙️ TECHNICAL SPECIFICATIONS • Pine Script Version: v6 • Maximum Objects: 500 lines, 500 labels, 500 boxes • Alert Functions: 8 independent alerts • Supported Timeframes: All (5-min recommended for Bar Count) • Compatibility: All TradingView plans, Mobile & Desktop ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🚀 RECOMMENDED INITIAL SETTINGS GAPS • Traditional Gap: ✓ • Tail Gap: ✓ • Border Width: 2 BAR COUNT • Use Bar Count: ✓ • Label Size: Normal EMA • EMA 20: ✓ • EMA 50: ✓ • EMA 100: ✓ • EMA 200: ✓ PREVIOUS VALUES • 1st: close (Previous close) • 2nd: high (Previous high) • 3rd: low (Previous low) INSIDE & OUTSIDE BAR • All patterns: ✓ • Label Size: Large ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🌟 WHY CHOOSE PABP? ✅ Solid Theoretical Foundation Based on Al Brooks' decades of trading experience ✅ Complete Professional Features Systematizes complex price action analysis ✅ Highly Customizable Every feature adjustable to personal style ✅ Excellent Performance Optimized code ensures smooth experience ✅ Continuous Updates Constantly improving based on feedback ✅ Suitable for All Levels Benefits beginners to professionals ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 RECOMMENDED LEARNING Al Brooks Books: • "Trading Price Action Trends" • "Trading Price Action Trading Ranges" • "Trading Price Action Reversals" Learning Path: 1. Understand basic candlestick patterns 2. Learn EMA applications 3. Master market structure analysis 4. Develop trading system 5. Continuous practice and optimization ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ ⚠️ RISK DISCLOSURE IMPORTANT NOTICE: • For educational and informational purposes only • Does not constitute investment advice • Past performance doesn't guarantee future results • Trading involves risk and may result in capital loss • Trade according to your risk tolerance • Test thoroughly in demo account first RESPONSIBLE TRADING: • Always use stop losses • Control position sizes reasonably • Don't overtrade • Continuous learning and improvement • Keep trading journal ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📜 COPYRIGHT Price Action Brooks Pro (PABP) Author: © JimmC98 License: Mozilla Public License 2.0 Pine Script Version: v6 Acknowledgments: Thanks to Dr. Al Brooks for his contributions to price action trading. This indicator is developed based on his theories. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Experience professional-grade price action analysis now! "The best traders read price action, not indicators. But when indicators help you read price action better, use them." - Al Brooks
Pine Script®指標
由JimmC98提供
1
Previous D/W/M HLOCHey traders, Here's a simple Multi-Timeframe indicator that essentially turns time and price into a box. It'll take the previous high, low, opening price, or closing price from one of the three timeframes of your choice (day, week, or month). For whatever reason I can't get the opening price to function consistently so if you find improvements feel free to let me know, this will help traders who prefer to use opening price over closing price. Naturally this form of charting is classical and nature and some key figures you could use to study its usage are - Richard W. Schabacker (1930s) - Edwards & Magee (1948) - Peter Brandt - Stacey Burke (more on the intraday side - typically our preference) It's usage put plainly: - Quantifying Accumulation or Distribution - Revealing Energy Build-Up (Compression) - Framing Breakouts and False Breakouts - Structuring Time - Identifying opportunities to trade a daily, weekly, or monthly range.
Pine Script®指標
由lfjaden提供
1
Volumen Abreviado📌 Indicator Description: Abbreviated Volume (K / M) This indicator displays each candle’s volume in an abbreviated format (K for thousands, M for millions, B for billions), making it easier to read and avoiding overly large numbers on the chart. Key Features: Volume histogram colored by candle direction (green: bullish, red: bearish, gray: neutral). Configurable volume average line. Label showing the abbreviated volume on the latest bar. Optimized Y-axis scale to display compact values. Perfect for: Traders who want to quickly read volume without being distracted by large numbers. Charts with high trading volume where full numbers are hard to read. Fast analysis in stocks, crypto, or futures markets. How to Use: Add the indicator to your chart. Adjust the average period in the settings. Toggle the last-bar label on or off based on your preference. ✅ Works with any time frame and market.
Pine Script®指標
由juliomillonario提供
3-Candle PDFThe Dynamic Fusion Indicator (DFI) is a powerful analytical tool designed to identify high-probability trading opportunities by combining trend momentum, volatility, and volume flow into one clear signal. It adapts in real time to changing market conditions, highlighting optimal entry and exit zones with intuitive color coding. The DFI filters out market noise using a hybrid smoothing algorithm, ensuring clarity even in choppy environments. Suitable for all timeframes and instruments, it helps traders anticipate reversals, confirm trends, and manage risk more effectively. Whether you’re scalping or swing trading, the DFI provides a confident, data-driven edge in any market.
Pine Script®指標
由umarmuhammad1提供
2-Candle PDFThe Dynamic Fusion Indicator (DFI) is a powerful analytical tool designed to identify high-probability trading opportunities by combining trend momentum, volatility, and volume flow into one clear signal. It adapts in real time to changing market conditions, highlighting optimal entry and exit zones with intuitive color coding. The DFI filters out market noise using a hybrid smoothing algorithm, ensuring clarity even in choppy environments. Suitable for all timeframes and instruments, it helps traders anticipate reversals, confirm trends, and manage risk more effectively. Whether you’re scalping or swing trading, the DFI provides a confident, data-driven edge in any market.
Pine Script®指標
由umarmuhammad1提供
cd_correlation_analys_Cxcd_correlation_analys_Cx General: This indicator is designed for correlation analysis by classifying stocks (487 in total) and indices (14 in total) traded on Borsa İstanbul (BIST) on a sectoral basis. Tradingview's sector classifications (20) have been strictly adhered to for sector grouping. Depending on user preference, the analysis can be performed within sectors, between sectors, or manually (single asset). Let me express my gratitude to the code author, @fikira, beforehand; you will find the reason for my thanks in the context. Details: First, let's briefly mention how this indicator could have been prepared using the classic method before going into details. Classically, assets could be divided into groups of forty (40), and the analysis could be performed using the built-in function: ta.correlation(source1, source2, length) → series float. I chose sectoral classification because I believe there would be a higher probability of assets moving together, rather than using fixed-number classes. In this case, 21 arrays were formed with the following number of elements: (3, 11, 21, 60, 29, 20, 12, 3, 31, 5, 10, 11, 6, 48, 73, 62, 16, 19, 13, 34 and indices (14)). However, you might have noticed that some arrays have more than 40 elements. This is exactly where @Fikira's indicator came to the rescue. When I examined their excellent indicator, I saw that it could process 120 assets in a single operation. (I believe this was the first limit overrun; thanks again.) It was amazing to see that data for 3 pairs could be called in a single request using a special method. You can find the details here: When I adapted it for BIST, I found it sufficient to call data for 2 pairs instead of 3 in a single go. Since asset prices are regular and have 2 decimal places, I used a fixed multiplier of $10^8$ and a fixed decimal count of 2 in Fikira's formulas. With this method, the (high, low, open, close) values became accessible for each asset. The summary up to this point is that instead of the ready-made formula + groups of 40, I used variable-sized groups and the method I will detail now. Correlation/harmony/co-movement between assets provides advantages to market participants. Coherent assets are expected to rise or fall simultaneously. Therefore, to convert co-movement into a mathematical value, I defined the possible movements of the current candle relative to the previous candle bar over a certain period (user-defined). These are: Up := high > high and low > low Down := high < high and low < low Inside := high <= high and low >= low Outside := high >= high and low <= low and NOT Inside. Ignore := high = low = open = close If both assets performed the same movement, 1 was added to the tracking counter. If (Up-Up), (Down-Down), (Inside-Inside), or (Outside-Outside), then counter := counter + 1. If the period length is 100 and the counter is 75, it means there is 75% co-movement. Corr = counter / period ($75/100$) Average = ta.sma(Corr, 100) is obtained. The highest coefficients recorded in the array are presented to the user in a table. From the user menu options, the user can choose to compare: • With assets in its own sector • With assets in the selected sector • By activating the confirmation box and manually entering a single asset for comparison. Table display options can be adjusted from the Settings tab. In the attached examples: Results for AKBNK stock from the Finance sector compared with GARAN stock from the same sector: Timeframe: Daily, Period: 50 => Harmony 76% (They performed the same movement in 38 out of 50 bars) Comment: Opposite movements at swing high and low levels may indicate a change in the direction of the price flow (SMT). Looking at ASELS from the Electronic Technology sector over the last 30 daily candles, they performed the same movements by 40% with XU100, 73.3% (22/30) with XUTEK (Technology Index), and 86.9% according to the averages. Comment: It is more appropriate to follow ASELS stock with XUTEK (Technology index) instead of the general index (XU100). Opposite movements at swing high and low levels may indicate a change in the direction of the price flow (SMT). Again, when ASELS stock is taken on H1 instead of daily, and the length is 100 instead of 30, the harmony rate is seen to be 87%. Please share your thoughts and criticisms regarding the indicator, which I prepared with a bit of an educational purpose specifically for BIST. Happy trading.
Pine Script®指標
由cdikici71提供
2
Ultimate Oscillator (ULTOSC)The Ultimate Oscillator (ULTOSC) is a technical momentum indicator developed by Larry Williams that combines three different time periods to reduce the volatility and false signals common in single-period oscillators. By using a weighted average of three Stochastic-like calculations across short, medium, and long-term periods, the Ultimate Oscillator provides a more comprehensive view of market momentum while maintaining sensitivity to price changes. The indicator addresses the common problem of oscillators being either too sensitive (generating many false signals) or too slow (missing opportunities). By incorporating multiple timeframes with decreasing weights for longer periods, ULTOSC attempts to capture both short-term momentum shifts and longer-term trend strength, making it particularly valuable for identifying divergences and potential reversal points. ## Core Concepts * **Multi-timeframe analysis:** Combines three different periods (typically 7, 14, 28) to capture various momentum cycles * **Weighted averaging:** Assigns higher weights to shorter periods for responsiveness while including longer periods for stability * **Buying pressure focus:** Measures the relationship between closing price and the true range rather than just high-low range * **Divergence detection:** Particularly effective at identifying momentum divergences that precede price reversals * **Normalized scale:** Oscillates between 0 and 100, with clear overbought/oversold levels ## Common Settings and Parameters | Parameter | Default | Function | When to Adjust | |-----------|---------|----------|---------------| | Fast Period | 7 | Short-term momentum calculation | Lower (5-6) for more sensitivity, higher (9-12) for smoother signals | | Medium Period | 14 | Medium-term momentum calculation | Adjust based on typical swing duration in the market | | Slow Period | 28 | Long-term momentum calculation | Higher values (35-42) for longer-term position trading | | Fast Weight | 4.0 | Weight applied to fast period | Higher weight increases short-term sensitivity | | Medium Weight | 2.0 | Weight applied to medium period | Adjust to balance medium-term influence | | Slow Weight | 1.0 | Weight applied to slow period | Usually kept at 1.0 as the baseline weight | **Pro Tip:** The classic 7/14/28 periods with 4/2/1 weights work well for most markets, but consider using 5/10/20 with adjusted weights for faster markets or 14/28/56 for longer-term analysis. ## Calculation and Mathematical Foundation **Simplified explanation:** The Ultimate Oscillator calculates three separate "buying pressure" ratios using different time periods, then combines them using weighted averaging. Buying pressure is defined as the close minus the true low, divided by the true range. **Technical formula:** ``` BP = Close - Min(Low, Previous Close) TR = Max(High, Previous Close) - Min(Low, Previous Close) BP_Sum_Fast = Sum(BP, Fast Period) TR_Sum_Fast = Sum(TR, Fast Period) Raw_Fast = 100 × (BP_Sum_Fast / TR_Sum_Fast) BP_Sum_Medium = Sum(BP, Medium Period) TR_Sum_Medium = Sum(TR, Medium Period) Raw_Medium = 100 × (BP_Sum_Medium / TR_Sum_Medium) BP_Sum_Slow = Sum(BP, Slow Period) TR_Sum_Slow = Sum(TR, Slow Period) Raw_Slow = 100 × (BP_Sum_Slow / TR_Sum_Slow) ULTOSC = 100 × / (Fast_Weight + Medium_Weight + Slow_Weight) ``` Where: - BP = Buying Pressure - TR = True Range - Fast Period = 7, Medium Period = 14, Slow Period = 28 (defaults) - Fast Weight = 4, Medium Weight = 2, Slow Weight = 1 (defaults) > 🔍 **Technical Note:** The implementation uses efficient circular buffers for all three period calculations, maintaining O(1) time complexity per bar. The algorithm properly handles true range calculations including gaps and ensures accurate buying pressure measurements across all timeframes. ## Interpretation Details ULTOSC provides several analytical perspectives: * **Overbought/Oversold conditions:** Values above 70 suggest overbought conditions, below 30 suggest oversold conditions * **Momentum direction:** Rising ULTOSC indicates increasing buying pressure, falling indicates increasing selling pressure * **Divergence analysis:** Divergences between ULTOSC and price often precede significant reversals * **Trend confirmation:** ULTOSC direction can confirm or question the prevailing price trend * **Signal quality:** Extreme readings (>80 or <20) indicate strong momentum that may be unsustainable * **Multiple timeframe consensus:** When all three underlying periods agree, signals are typically more reliable ## Trading Applications **Primary Uses:** - **Divergence trading:** Identify when momentum diverges from price for reversal signals - **Overbought/oversold identification:** Find potential entry/exit points at extreme levels - **Trend confirmation:** Validate breakouts and trend continuations - **Momentum analysis:** Assess the strength of current price movements **Advanced Strategies:** - **Multi-divergence confirmation:** Look for divergences across multiple timeframes - **Momentum breakouts:** Trade when ULTOSC breaks above/below key levels with volume - **Swing trading entries:** Use oversold/overbought levels for swing position entries - **Trend strength assessment:** Evaluate trend quality using momentum consistency ## Signal Combinations **Strong Bullish Signals:** - ULTOSC rises from oversold territory (<30) with positive price divergence - ULTOSC breaks above 50 after forming a base near 30 - All three underlying periods show increasing buying pressure **Strong Bearish Signals:** - ULTOSC falls from overbought territory (>70) with negative price divergence - ULTOSC breaks below 50 after forming a top near 70 - All three underlying periods show decreasing buying pressure **Divergence Signals:** - **Bullish divergence:** Price makes lower lows while ULTOSC makes higher lows - **Bearish divergence:** Price makes higher highs while ULTOSC makes lower highs - **Hidden bullish divergence:** Price makes higher lows while ULTOSC makes lower lows (trend continuation) - **Hidden bearish divergence:** Price makes lower highs while ULTOSC makes higher highs (trend continuation) ## Comparison with Related Oscillators | Indicator | Periods | Focus | Best Use Case | |-----------|---------|-------|---------------| | **Ultimate Oscillator** | 3 periods | Buying pressure | Divergence detection | | **Stochastic** | 1-2 periods | Price position | Overbought/oversold | | **RSI** | 1 period | Price momentum | Momentum analysis | | **Williams %R** | 1 period | Price position | Short-term signals | ## Advanced Configurations **Fast Trading Setup:** - Fast: 5, Medium: 10, Slow: 20 - Weights: 4/2/1, Thresholds: 75/25 **Standard Setup:** - Fast: 7, Medium: 14, Slow: 28 - Weights: 4/2/1, Thresholds: 70/30 **Conservative Setup:** - Fast: 14, Medium: 28, Slow: 56 - Weights: 3/2/1, Thresholds: 65/35 **Divergence Focused:** - Fast: 7, Medium: 14, Slow: 28 - Weights: 2/2/2, Thresholds: 70/30 ## Market-Specific Adjustments **Volatile Markets:** - Use longer periods (10/20/40) to reduce noise - Consider higher threshold levels (75/25) - Focus on extreme readings for signal quality **Trending Markets:** - Emphasize divergence analysis over absolute levels - Look for momentum confirmation rather than reversal signals - Use hidden divergences for trend continuation **Range-Bound Markets:** - Standard overbought/oversold levels work well - Trade reversals from extreme levels - Combine with support/resistance analysis ## Limitations and Considerations * **Lagging component:** Contains inherent lag due to multiple moving average calculations * **Complex calculation:** More computationally intensive than single-period oscillators * **Parameter sensitivity:** Performance varies significantly with different period/weight combinations * **Market dependency:** Most effective in trending markets with clear momentum patterns * **False divergences:** Not all divergences lead to significant price reversals * **Whipsaw potential:** Can generate conflicting signals in choppy markets ## Best Practices **Effective Usage:** - Focus on divergences rather than absolute overbought/oversold levels - Combine with trend analysis for context - Use multiple timeframe analysis for confirmation - Pay attention to the speed of momentum changes **Common Mistakes:** - Over-relying on overbought/oversold levels in strong trends - Ignoring the underlying trend direction - Using inappropriate period settings for the market being analyzed - Trading every divergence without additional confirmation **Signal Enhancement:** - Combine with volume analysis for confirmation - Use price action context (support/resistance levels) - Consider market volatility when setting thresholds - Look for convergence across multiple momentum indicators ## Historical Context and Development The Ultimate Oscillator was developed by Larry Williams and introduced in his 1985 article "The Ultimate Oscillator" in Technical Analysis of Stocks and Commodities magazine. Williams designed it to address the limitations of single-period oscillators by: - Reducing false signals through multi-timeframe analysis - Maintaining sensitivity to short-term momentum changes - Providing more reliable divergence signals - Creating a more robust momentum measurement tool The indicator has become a standard tool in technical analysis, particularly valued for its divergence detection capabilities and its balanced approach to momentum measurement. ## References * Williams, L. R. (1985). The Ultimate Oscillator. Technical Analysis of Stocks and Commodities, 3(4). * Williams, L. R. (1999). Long-Term Secrets to Short-Term Trading. Wiley Trading.
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Standardization (Z-score)Standardization, often referred to as Z-score normalization, is a data preprocessing technique that rescales data to have a mean of 0 and a standard deviation of 1. The resulting values, known as Z-scores, indicate how many standard deviations an individual data point is from the mean of the dataset (or a rolling sample of it). This indicator calculates and plots the Z-score for a given input series over a specified lookback period. It is a fundamental tool for statistical analysis, outlier detection, and preparing data for certain machine learning algorithms. ## Core Concepts * **Standardization:** The process of transforming data to fit a standard normal distribution (or more generally, to have a mean of 0 and standard deviation of 1). * **Z-score (Standard Score):** A dimensionless quantity that represents the number of standard deviations by which a data point deviates from the mean of its sample. The formula for a Z-score is: `Z = (x - μ) / σ` Where: * `x` is the individual data point (e.g., current value of the source series). * `μ` (mu) is the mean of the sample (calculated over the lookback period). * `σ` (sigma) is the standard deviation of the sample (calculated over the lookback period). * **Mean (μ):** The average value of the data points in the sample. * **Standard Deviation (σ):** A measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. ## Common Settings and Parameters | Parameter | Type | Default | Function | When to Adjust | | :-------------- | :----------- | :------ | :------------------------------------------------------------------------------------------------------ | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Source | series float | close | The input data series (e.g., price, volume, indicator values). | Choose the series you want to standardize. | | Lookback Period | int | 20 | The number of bars (sample size) used for calculating the mean (μ) and standard deviation (σ). Min 2. | A larger period provides more stable estimates of μ and σ but will be less responsive to recent changes. A shorter period is more reactive. `minval` is 2 because `ta.stdev` requires it. | **Pro Tip:** Z-scores are excellent for identifying anomalies or extreme values. For instance, applying Standardization to trading volume can help quickly spot days with unusually high or low activity relative to the recent norm (e.g., Z-score > 2 or < -2). ## Calculation and Mathematical Foundation The Z-score is calculated for each bar as follows, using a rolling window defined by the `Lookback Period`: 1. **Calculate Mean (μ):** The simple moving average (`ta.sma`) of the `Source` data over the specified `Lookback Period` is calculated. This serves as the sample mean `μ`. `μ = ta.sma(Source, Lookback Period)` 2. **Calculate Standard Deviation (σ):** The standard deviation (`ta.stdev`) of the `Source` data over the same `Lookback Period` is calculated. This serves as the sample standard deviation `σ`. `σ = ta.stdev(Source, Lookback Period)` 3. **Calculate Z-score:** * If `σ > 0`: The Z-score is calculated using the formula: `Z = (Current Source Value - μ) / σ` * If `σ = 0`: This implies all values in the lookback window are identical (and equal to the mean). In this case, the Z-score is defined as 0, as the current source value is also equal to the mean. * If `σ` is `na` (e.g., insufficient data in the lookback period), the Z-score is `na`. > 🔍 **Technical Note:** > * The `Lookback Period` must be at least 2 for `ta.stdev` to compute a valid standard deviation. > * The Z-score calculation uses the sample mean and sample standard deviation from the rolling lookback window. ## Interpreting the Z-score * **Magnitude and Sign:** * A Z-score of **0** means the data point is identical to the sample mean. * A **positive Z-score** indicates the data point is above the sample mean. For example, Z = 1 means the point is 1 standard deviation above the mean. * A **negative Z-score** indicates the data point is below the sample mean. For example, Z = -1 means the point is 1 standard deviation below the mean. * **Typical Range:** For data that is approximately normally distributed (bell-shaped curve): * About 68% of Z-scores fall between -1 and +1. * About 95% of Z-scores fall between -2 and +2. * About 99.7% of Z-scores fall between -3 and +3. * **Outlier Detection:** Z-scores significantly outside the -2 to +2 range, and especially outside -3 to +3, are often considered outliers or extreme values relative to the recent historical data in the lookback window. * **Volatility Indication:** When applied to price, large absolute Z-scores can indicate moments of high volatility or significant deviation from the recent price trend. The indicator plots horizontal lines at ±1, ±2, and ±3 standard deviations to help visualize these common thresholds. ## Common Applications 1. **Outlier Detection:** Identifying data points that are unusual or extreme compared to the rest of the sample. This is a primary use in financial markets for spotting abnormal price moves, volume spikes, etc. 2. **Comparative Analysis:** Allows for comparison of scores from different distributions that might have different means and standard deviations. For example, comparing the Z-score of returns for two different assets. 3. **Feature Scaling in Machine Learning:** Standardizing features to have a mean of 0 and standard deviation of 1 is a common preprocessing step for many machine learning algorithms (e.g., SVMs, logistic regression, neural networks) to improve performance and convergence. 4. **Creating Normalized Oscillators:** The Z-score itself can be used as a bounded (though not strictly between -1 and +1) oscillator, indicating how far the current price has deviated from its moving average in terms of standard deviations. 5. **Statistical Process Control:** Used in quality control charts to monitor if a process is within expected statistical limits. ## Limitations and Considerations * **Assumption of Normality for Probabilistic Interpretation:** While Z-scores can always be calculated, the probabilistic interpretations (e.g., "68% of data within ±1σ") strictly apply to normally distributed data. Financial data is often not perfectly normal (e.g., it can have fat tails). * **Sensitivity of Mean and Standard Deviation to Outliers:** The sample mean (μ) and standard deviation (σ) used in the Z-score calculation can themselves be influenced by extreme outliers within the lookback period. This can sometimes mask or exaggerate the Z-score of other points. * **Choice of Lookback Period:** The Z-score is highly dependent on the `Lookback Period`. A short period makes it very sensitive to recent fluctuations, while a long period makes it smoother and less responsive. The appropriate period depends on the analytical goal. * **Stationarity:** For time series data, Z-scores are calculated based on a rolling window. This implicitly assumes some level of local stationarity (i.e., the mean and standard deviation are relatively stable within the window).
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Triangular Moving Average (TRIMA)The Triangular Moving Average (TRIMA) is a technical indicator that applies a triangular weighting scheme to price data, providing enhanced smoothing compared to simpler moving averages. Originating in the early 1970s as technical analysts sought more effective noise filtering methods, the TRIMA was first popularized through the work of market technician Arthur Merrill. Its formal mathematical properties were established in the 1980s, and the indicator gained widespread adoption in the 1990s as computerized charting became standard. TRIMA effectively filters out market noise while maintaining important trends through its unique center-weighted calculation method. ## Core Concepts * **Double-smoothing process:** TRIMA can be viewed as applying a simple moving average twice, creating more effective noise filtering * **Triangular weighting:** Uses a symmetrical weight distribution that emphasizes central data points and reduces emphasis toward both ends * **Constant-time implementation:** Two $O(1)$ SMA passes with circular buffers preserve exact triangular weights while keeping update cost constant per bar * **Market application:** Particularly effective for identifying the underlying trend in noisy market conditions where standard moving averages generate too many false signals * **Timeframe flexibility:** Works across multiple timeframes, with longer periods providing cleaner trend signals in higher timeframes The core innovation of TRIMA is its unique triangular weighting scheme, which can be viewed either as a specialized weight distribution or as a twice-applied simple moving average with adjusted period. This creates more effective noise filtering without the excessive lag penalty typically associated with longer-period averages. The symmetrical nature of the weight distribution ensures zero phase distortion, preserving the timing of important market turning points. ## Common Settings and Parameters | Parameter | Default | Function | When to Adjust | |-----------|---------|----------|---------------| | Length | 14 | Controls the lookback period | Increase for smoother signals in volatile markets, decrease for responsiveness | | Source | close | Price data used for calculation | Consider using hlc3 for a more balanced price representation | **Pro Tip:** For a good balance between smoothing and responsiveness, try using a TRIMA with period N instead of an SMA with period 2N - you'll get similar smoothing characteristics but with less lag. ## Calculation and Mathematical Foundation **Simplified explanation:** TRIMA calculates a weighted average of prices where the weights form a triangle shape. The middle prices get the most weight, and weights gradually decrease toward both the recent and older ends. This creates a smooth filter that effectively removes random price fluctuations while preserving the underlying trend. **Technical formula:** TRIMA = Σ(Price × Weight ) / Σ(Weight ) Where the triangular weights form a symmetric pattern: - Weight = min(i, n-1-i) + 1 - Example for n=5: weights = - Example for n=4: weights = Alternatively, TRIMA can be calculated as: TRIMA(source, p) = SMA(SMA(source, (p+1)/2), (p+1)/2) > 🔍 **Technical Note:** The double application of SMA explains why TRIMA provides better smoothing than a single SMA or WMA. This approach effectively applies smoothing twice with optimal period adjustment, creating a -18dB/octave roll-off in the frequency domain compared to -6dB/octave for a simple moving average, and the current implementation achieves $O(1)$ complexity through circular buffers and NA-safe warmup compensation. ## Interpretation Details TRIMA can be used in various trading strategies: * **Trend identification:** The direction of TRIMA indicates the prevailing trend * **Signal generation:** Crossovers between price and TRIMA generate trade signals with fewer false alarms than SMA * **Support/resistance levels:** TRIMA can act as dynamic support during uptrends and resistance during downtrends * **Trend strength assessment:** Distance between price and TRIMA can indicate trend strength * **Multiple timeframe analysis:** Using TRIMAs with different periods can confirm trends across different timeframes ## Limitations and Considerations * **Market conditions:** Like all moving averages, less effective in choppy, sideways markets * **Lag factor:** More lag than WMA or EMA due to center-weighted emphasis * **Limited adaptability:** Fixed weighting scheme cannot adapt to changing market volatility * **Response time:** Takes longer to reflect sudden price changes than directionally-weighted averages * **Complementary tools:** Best used with momentum oscillators or volume indicators for confirmation ## References * Ehlers, John F. "Cycle Analytics for Traders." Wiley, 2013 * Kaufman, Perry J. "Trading Systems and Methods." Wiley, 2013 * Colby, Robert W. "The Encyclopedia of Technical Market Indicators." McGraw-Hill, 2002
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Savitzky-Golay Filter (SGF)The Savitzky-Golay Filter (SGF) is a digital filter that performs local polynomial regression on a series of values to determine the smoothed value for each point. Developed by Abraham Savitzky and Marcel Golay in 1964, it is particularly effective at preserving higher moments of the data while reducing noise. This implementation provides a practical adaptation for financial time series, offering superior preservation of peaks, valleys, and other important market structures that might be distorted by simpler moving averages. ## Core Concepts * **Local polynomial fitting:** Fits a polynomial of specified order to a sliding window of data points * **Moment preservation:** Maintains higher statistical moments (peaks, valleys, inflection points) * **Optimized coefficients:** Uses pre-computed coefficients for common polynomial orders * **Adaptive weighting:** Weight distribution varies based on polynomial order and window size * **Market application:** Particularly effective for preserving significant price movements while filtering noise The core innovation of the Savitzky-Golay filter is its ability to smooth data while preserving important features that are often flattened by other filtering methods. This makes it especially valuable for technical analysis where maintaining the shape of price patterns is crucial. ## Common Settings and Parameters | Parameter | Default | Function | When to Adjust | |-----------|---------|----------|---------------| | Window Size | 11 | Number of points used in local fitting (must be odd) | Increase for smoother output, decrease for better feature preservation | | Polynomial Order | 2 | Order of fitting polynomial (2 or 4) | Use 2 for general smoothing, 4 for better peak preservation | | Source | close | Price data used for calculation | Consider using hlc3 for more stable fitting | **Pro Tip:** A window size of 11 with polynomial order 2 provides a good balance between smoothing and feature preservation. For sharper peaks and valleys, use order 4 with a smaller window size. ## Calculation and Mathematical Foundation **Simplified explanation:** The filter fits a polynomial of specified order to a moving window of price data. The smoothed value at each point is computed from this local fit, effectively removing noise while preserving the underlying shape of the data. **Technical formula:** For a window of size N and polynomial order M, the filtered value is: y = Σ(c_i × x ) Where: - c_i are the pre-computed filter coefficients - x are the input values in the window - Coefficients depend on window size N and polynomial order M > 🔍 **Technical Note:** The implementation uses optimized coefficient calculations for orders 2 and 4, which cover most practical applications while maintaining computational efficiency. ## Interpretation Details The Savitzky-Golay filter can be used in various trading strategies: * **Pattern recognition:** Preserves chart patterns while removing noise * **Peak detection:** Maintains amplitude and width of significant peaks * **Trend analysis:** Smooths price movement without distorting important transitions * **Divergence trading:** Better preservation of local maxima and minima * **Volatility analysis:** Accurate representation of price movement dynamics ## Limitations and Considerations * **Computational complexity:** More intensive than simple moving averages * **Edge effects:** First and last few points may show end effects * **Parameter sensitivity:** Performance depends on appropriate window size and order selection * **Data requirements:** Needs sufficient points for polynomial fitting * **Complementary tools:** Best used with volume analysis and momentum indicators ## References * Savitzky, A., Golay, M.J.E. "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Analytical Chemistry, 1964 * Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing," Chapter 14 * Schafer, R.W. "What Is a Savitzky-Golay Filter?" IEEE Signal Processing Magazine, 2011
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Bilateral Filter (BILATERAL)The Bilateral Filter is an edge-preserving smoothing technique that combines spatial filtering with intensity filtering to achieve noise reduction while maintaining significant price structure. Originally developed in computer vision for image processing, this adaptive filter has been adapted for financial time series analysis to provide superior smoothing that preserves important market transitions. The filter intelligently reduces noise in stable price regions while preserving sharp transitions like breakouts, reversals, and other significant market structures that would be blurred by conventional filters. ## Core Concepts * **Dual-domain filtering:** Combines traditional time-based (spatial) filtering with value-based (range) filtering for adaptive smoothing * **Edge preservation:** Maintains important price transitions while aggressively smoothing areas of minor fluctuation * **Adaptive processing:** Automatically adjusts filtering strength based on local price characteristics The core innovation of the Bilateral Filter is its ability to distinguish between random noise and significant price movements. Unlike conventional filters that smooth everything equally, Bilateral filtering preserves major price transitions by reducing the influence of price points that differ significantly from the current price, effectively preserving market structure while still eliminating noise. ## Common Settings and Parameters | Parameter | Default | Function | When to Adjust | |-----------|---------|----------|---------------| | Length | 14 | Controls the lookback window size | Increase for more context in filtering decisions, decrease for quicker response | | Sigma_S_Ratio | 0.3 | Controls spatial (time) weighting | Lower values emphasize recent bars, higher values distribute influence more evenly | | Sigma_R_Mult | 2.0 | Controls range (price) sensitivity | Lower values increase edge preservation, higher values increase smoothing | | Source | close | Price data used for calculation | Consider using hlc3 for a more balanced price representation | **Pro Tip:** For breakout trading strategies, try reducing Sigma_R_Mult to 1.0-1.5 to make the filter more sensitive to significant price moves, allowing it to preserve breakout signals while still filtering noise. ## Calculation and Mathematical Foundation **Simplified explanation:** The Bilateral Filter calculates a weighted average of nearby prices, where the weights depend on two factors: how far away in time the price point is (spatial weight) and how different the price value is (range weight). Points that are close in time AND similar in value get the highest weight. This means stable price regions get smoothed while significant changes are preserved. **Technical formula:** BF = (1 / Wp) × Σ_{q ∈ S} G_s(||p - q||) × G_r(|I - I |) × I Where: - G_s is the spatial Gaussian kernel: exp(-||p - q||² / (2 × σ_s²)) - G_r is the range Gaussian kernel: exp(-|I - I |² / (2 × σ_r²)) - Wp is the normalization factor (sum of all weights) > 🔍 **Technical Note:** The sigma_r parameter is typically calculated dynamically based on local price volatility (standard deviation) to provide adaptive filtering - this automatically adjusts filtering strength based on market conditions. ## Interpretation Details The Bilateral Filter can be applied in various trading contexts: * **Trend identification:** Reveals cleaner underlying price direction by removing noise while preserving trend changes * **Support/resistance identification:** Provides clearer price levels by preserving significant turning points * **Pattern recognition:** Maintains critical chart patterns while eliminating distracting minor fluctuations * **Breakout trading:** Preserves sharp price transitions for more reliable breakout signals * **Pre-processing:** Can be used as an initial filter before applying other technical indicators to reduce false signals ## Limitations and Considerations * **Computational complexity:** More intensive calculations than traditional linear filters * **Parameter sensitivity:** Performance highly dependent on proper parameter selection * **Non-linearity:** Non-linear behavior may produce unexpected results in certain market conditions * **Interpretation adjustment:** Requires different interpretation than conventional moving averages * **Complementary tools:** Best used alongside volume analysis and traditional indicators for confirmation ## References * Tomasi, C. and Manduchi, R. "Bilateral Filtering for Gray and Color Images," Proceedings of IEEE ICCV, 1998 * Paris, S. et al. "A Gentle Introduction to Bilateral Filtering and its Applications," ACM SIGGRAPH, 2008
Pine Script®指標
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