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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.
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fract tarafından
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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
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Amjad_S tarafından
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.
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thequantscience tarafından