MathHelpersLibrary "MathHelpers"
Overview
A collection of helper functions for designing indicators and strategies.
calculateATR(length, log)
Calculates the Average True Range (ATR) or Log ATR based on the 'log' parameter. Sans Wilder's Smoothing
Parameters:
length (simple int)
log (simple bool)
Returns: float The calculated ATR value. Returns Log ATR if `log` is true, otherwise returns standard ATR.
CDF(z)
Computes the Cumulative Distribution Function (CDF) for a given value 'z', mimicking the CDF function in "Statistically Sound Indicators" by Timothy Masters.
Parameters:
z (simple float)
Returns: float The CDF value corresponding to the input `z`, ranging between 0 and 1.
logReturns(lookback)
Calculates the logarithmic returns over a specified lookback period.
Parameters:
lookback (simple int)
Returns: float The calculated logarithmic return. Returns `na` if insufficient data is available.
Maths
Weierstrass Function (Fractal Cycles)THE WEIERSTRASS FUNCTION
f(x) = ∑(n=0)^∞ a^n * cos(b^n * π * x)
The Weierstrass Function is the sum of an infinite series of cosine functions, each with increasing frequency and decreasing amplitude. This creates powerful multi-scale oscillations within the range ⬍(-2;+2), resembling a system of self-repetitive patterns. You can zoom into any part of the output and observe similar proportions, mimicking the hidden order behind the irregularity and unpredictability of financial markets.
IT DOESN’T RELY ON ANY MARKET DATA, AS THE OUTPUT IS BASED PURELY ON A MATHEMATICAL FORMULA!
This script does not provide direct buy or sell signals and should be used as a tool for analyzing the market behavior through fractal geometry. The function is often used to model complex, chaotic systems, including natural phenomena and financial markets.
APPLICATIONS:
Timing Aspect: Identifies the phases of market cycles, helping to keep awareness of frequency of turning points
Price-Modeling features: The Amplitude, frequency, and scaling settings allow the indicator to simulate the trends and oscillations. Its nowhere-differentiable nature aligns with the market's inherent uncertainty. The fractured oscillations resemble sharp jumps, noise, and dips found in volatile markets.
SETTINGS
Amplitude Factor (a): Controls the size of each wave. A higher value makes the waves larger.
Frequency Factor (b): Determines how fast the waves oscillate. A higher value creates more frequent waves.
Ability to Invert the output: Just like any cosine function it starts its journey with a decline, which is not distinctive to the behavior of most assets. The default setting is in "inverted mode".
Scale Factor: Adjusts the speed at which the oscillations grow over time.
Number of Terms (n_terms): Increases the number of waves. More terms add complexity to the pattern.
MathOperatorLibrary "MathOperator"
Methods to handle operators.
method add(value_a, value_b)
Add value a to b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method subtract(value_a, value_b)
subtract value b from a.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method multiply(value_a, value_b)
multiply value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method divide(value_a, value_b)
divide value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method remainder(value_a, value_b)
remainder of a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method equal(value_a, value_b)
equality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method not_equal(value_a, value_b)
inequality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over(value_a, value_b)
value a is over b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under(value_a, value_b)
value a is under b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over_equal(value_a, value_b)
value a is over equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under_equal(value_a, value_b)
value a is under equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method and_(value_a, value_b)
logical and of a with b
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method or_(value_a, value_b)
logical or of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method not_(value_a)
logical not of a.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
Returns: bool.
method xor_(value_a, value_b)
logical xor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method xnor_(value_a, value_b)
logical xnor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nand_(value_a, value_b)
logical nand of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nor_(value_a, value_b)
logical nor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
Guassian Distribution Forecast [prediction intervals]The Indicator
The Indicator combines volatility and frequency distributions to forecast an area of possible price expansion with an approximate confidence interval / level and level of significance (significance level).
The Script Formula
Additional comments
To alter the models forecasting precision to reflect a given confidence interval, e.g the 90% confidence level (C.L.), use the 1.64 multiplier (toggle value in "Standard normal distribution sd" setting), to use a specific C.L., e.g. the 85th percentile either search for this on google, or calculate it yourself using a Standard Normal Distribution Probability table. Additionaly volatility may be changed by toggling the lookback period setting, this can be thought of as widening the distribution tails.
The look forward parameter is currently fixed at 20, this is because it does not currently work correctly with higher integers, I will try resolve this problem and any other bugs as soon as possible
Autocorrelation - The Quant ScienceAutocorrelation - The Quant Science it is an indicator developed to quickly calculate the autocorrelation of a historical series. The objective of this indicator is to plot the autocorrelation values and highlight market moments where the value is positive and exceeds the attention threshold.
This indicator can be used for manual analysis when a trader needs to search for new price patterns within the historical series or to create complex formulas in estimating future prices.
What is autocorrelation?
Autocorrelation in trading is a statistical measure used to determine the presence of a relationship or pattern of dependence between values in a financial time series over time. It represents the correlation of past values in a series with its future values. In other words, autocorrelation in trading aims to identify if there are systematic relationships between the past prices or returns of a security or market and its future prices or returns. This analysis can be helpful in identifying patterns or trends that can be leveraged for informed trading decisions. The presence of autocorrelation may suggest that market prices or returns follow a certain pattern or trend over time.
Limitations of the model
It is important to note that autocorrelation does not necessarily imply a causal relationship between past and future values. Other variables or market factors may influence the dynamics of prices or returns, and therefore autocorrelation could be merely a random coincidence. Therefore, it is essential to carefully evaluate the results of autocorrelation analysis along with other information and trading strategies to make informed decisions.
How to use
The usage is very simple, you just need to add it to the current chart to activate the indicator.
From the user interface, you can manage two important features:
1. Lenght: the delay period applied to the historical series during the autocorrelation calculation can be managed from the user interface. By default, it is set to 20, which means that the autocorrelation ratio within the historical series is calculated with a delay of 20 bars.
2. Threshold: the threshold value that the autocorrelation level must meet can be managed from the user interface. By default, it is set to 0.50, which means that the autocorrelation value must be higher than this threshold to be considered valid and displayed on the chart.
3. Bar color: the color used to display the autocorrelation data and highlight the bars when autocorrelation is valid can be managed from the user interface.
To set up the chart
We recommend disabling the 'wick' and 'border' of the candlesticks from the chart settings for a high-quality user experience.
Source CorrelationIn this small indicator I make it possible for the user to set two different input sources. Then, the indicator displays the correlation of these two input sources. It's a very small script, but I think it could be helpful to somebody to find uncorrelated indicators for his trading strategy. To use uncorrelated indicators is in general recommended.
Enjoy this small, but powerful tool. 🧙♂️
