OPEN-SOURCE SCRIPT
已更新 Mean and Standard Deviation Lines
Description:
Calculates the mean and standard deviation of close-to-close price differences over a specified period, providing insights into price volatility and potential breakouts.
Manually calculates mean and standard deviation for a deeper understanding of statistical concepts.
Plots the mean line, upper bound (mean + standard deviation), and lower bound (mean - standard deviation) to visualize price behavior relative to these levels.
Highlights bars that cross the upper or lower bounds with green (above) or red (below) triangles for easy identification of potential breakouts or breakdowns.
Customizable period input allows for analysis of short-term or long-term volatility patterns.
Probability Interpretations based on Standard Deviation:
50% probability: mean or expected value
68% probability: Values within 1 standard deviation of the mean (mean ± stdev) represent roughly 68% of the data in a normal distribution. This implies that around 68% of closing prices in the past period fell within this range.
95% probability: Expanding to 2 standard deviations (mean ± 2*stdev) captures approximately 95% of the data. So, in theory, there's a 95% chance that future closing prices will fall within this wider range.
99.7% probability: Going further to 3 standard deviations (mean ± 3*stdev) encompasses nearly 99.7% of the data. However, these extreme values become less likely as you move further away from the mean.
Key Features:
Uses manual calculations for mean and standard deviation, providing a hands-on approach.
Excludes the current bar's close price from calculations for more accurate analysis of past data.
Ensures valid index usage for robust calculation logic.
Employs unbiased standard deviation calculation for better statistical validity.
Offers clear visual representation of mean and volatility bands.
Considerations:
Manual calculations might have a slight performance impact compared to built-in functions.
Not a perfect normal distribution: Financial markets often deviate from a perfect normal distribution. This means probability interpretations based on standard deviation shouldn't be taken as absolute truths.
Non-stationarity: Market conditions and price behavior can change over time, impacting the validity of past data as a future predictor.
Other factors: Many other factors influence price movements beyond just the mean and standard deviation.
Always consider other technical and fundamental factors when making trading decisions.
Potential Use Cases:
Identifying periods of high or low volatility.
Discovering potential breakout or breakdown opportunities.
Comparing volatility across different timeframes.
Complementing other technical indicators for confirmation.
Understanding statistical concepts for financial analysis.
Calculates the mean and standard deviation of close-to-close price differences over a specified period, providing insights into price volatility and potential breakouts.
Manually calculates mean and standard deviation for a deeper understanding of statistical concepts.
Plots the mean line, upper bound (mean + standard deviation), and lower bound (mean - standard deviation) to visualize price behavior relative to these levels.
Highlights bars that cross the upper or lower bounds with green (above) or red (below) triangles for easy identification of potential breakouts or breakdowns.
Customizable period input allows for analysis of short-term or long-term volatility patterns.
Probability Interpretations based on Standard Deviation:
50% probability: mean or expected value
68% probability: Values within 1 standard deviation of the mean (mean ± stdev) represent roughly 68% of the data in a normal distribution. This implies that around 68% of closing prices in the past period fell within this range.
95% probability: Expanding to 2 standard deviations (mean ± 2*stdev) captures approximately 95% of the data. So, in theory, there's a 95% chance that future closing prices will fall within this wider range.
99.7% probability: Going further to 3 standard deviations (mean ± 3*stdev) encompasses nearly 99.7% of the data. However, these extreme values become less likely as you move further away from the mean.
Key Features:
Uses manual calculations for mean and standard deviation, providing a hands-on approach.
Excludes the current bar's close price from calculations for more accurate analysis of past data.
Ensures valid index usage for robust calculation logic.
Employs unbiased standard deviation calculation for better statistical validity.
Offers clear visual representation of mean and volatility bands.
Considerations:
Manual calculations might have a slight performance impact compared to built-in functions.
Not a perfect normal distribution: Financial markets often deviate from a perfect normal distribution. This means probability interpretations based on standard deviation shouldn't be taken as absolute truths.
Non-stationarity: Market conditions and price behavior can change over time, impacting the validity of past data as a future predictor.
Other factors: Many other factors influence price movements beyond just the mean and standard deviation.
Always consider other technical and fundamental factors when making trading decisions.
Potential Use Cases:
Identifying periods of high or low volatility.
Discovering potential breakout or breakdown opportunities.
Comparing volatility across different timeframes.
Complementing other technical indicators for confirmation.
Understanding statistical concepts for financial analysis.
版本注释
made some changes on how the mean and standard deviation are calculated and I think this time it works.版本注释
changed some colors for clarity and make some correction to the descriptions.版本注释
updated the math. This indicator is a work in progress so be careful when you use it.版本注释
changed default period length to 100.版本注释
cleaned up the script and added copyright info.版本注释
Improved the math and removed anomaly detection to keep the script consistent with its name. 版本注释
corrected the math and renamed period into window because it is more appropriate. The window represents the analysis window for the transform pricing model which takes the statistical properties of the past and uses them to make predictions on the future price.版本注释
Updated the code to use built-in functions to calculate sample statistics and added a new variable so the analysis window for the mean is separate from the analysis window of standard deviation. Mean is now renamed to expected value.版本注释
removed link for compliance.版本注释
updated the license to CC BY-NC-ND 4.0开源脚本
本着TradingView的真正精神，此脚本的创建者将其开源，以便交易者可以查看和验证其功能。向作者致敬！虽然您可以免费使用它，但请记住，重新发布代码必须遵守我们的网站规则。
免责声明
这些信息和出版物并不意味着也不构成TradingView提供或认可的金融、投资、交易或其它类型的建议或背书。请在使用条款阅读更多信息。
免责声明
这些信息和出版物并不意味着也不构成TradingView提供或认可的金融、投资、交易或其它类型的建议或背书。请在使用条款阅读更多信息。