PaddingThe Padding library is a comprehensive and flexible toolkit designed to extend time series data within TradingView, making it an indispensable resource for advanced signal processing tasks such as FFT, filtering, convolution, and wavelet analysis. At its core, the library addresses the common challenge of edge effects by "padding" your data—that is, by appending additional data points beyond the natural boundaries of your original dataset. This extension not only mitigates the distortions that can occur at the endpoints but also helps to maintain the integrity of various transformations and calculations performed on the series. The library accomplishes this while preserving the ordering of your data, ensuring that the most recent point always resides at index 0.
Central to the functionality of this library are two key enumerations: Direction and PaddingType. The Direction enum determines where the padding will be applied. You can choose to extend the data in the forward direction (ahead of the current values), in the backward direction (behind the current values), or in both directions simultaneously. The PaddingType enum defines the specific method used for extending the data. The library supports several methods—including symmetric, reflect, periodic, antisymmetric, antireflect, smooth, constant, and zero padding—each of which has been implemented to suit different analytical scenarios. For instance, symmetric padding mirrors the original data across its boundaries, while reflect padding continues the trend by reflecting around endpoint values. Periodic padding repeats the data, and antisymmetric padding mirrors the data with alternating signs to counterbalance it. The antireflect and smooth methods take into account the derivatives of your data, thereby extending the series in a way that preserves or smoothly continues these derivative values. Constant and zero padding simply extend the series using fixed endpoint values or zeros. Together, these enums allow you to fine-tune how your data is extended, ensuring that the padding method aligns with the specific requirements of your analysis.
The library is designed to work with both single variable inputs and array inputs. When using array-based methods—particularly with the antireflect and smooth padding types—please note that the implementation intentionally discards the last data point as a result of the delta computation process. This behavior is an important consideration when integrating the library into your TradingView studies, as it affects the overall data length of the padded series. Despite this, the library’s structure and documentation make it straightforward to incorporate into your existing scripts. You simply provide your data source, define the length of your data window, and select the desired padding type and direction, along with any optional parameters to control the extent of the padding (using both_period, forward_period, or backward_period).
In practical application, the Padding library enables you to extend historical data beyond its original range in a controlled and predictable manner. This is particularly useful when preparing datasets for further signal processing, as it helps to reduce artifacts that can otherwise compromise the results of your analytical routines. Whether you are an experienced Pine Script developer or a trader exploring advanced data analysis techniques, this library offers a robust solution that enhances the reliability and accuracy of your studies by ensuring your algorithms operate on a more complete and well-prepared dataset.
Library "Padding"
A comprehensive library for padding time series data with various methods. Supports both single variable and array inputs, with flexible padding directions and periods. Designed for signal processing applications including FFT, filtering, convolution, and wavelets. All methods maintain data ordering with most recent point at index 0.
symmetric(source, series_length, direction, both_period, forward_period, backward_period)
Applies symmetric padding by mirroring the input data across boundaries
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with symmetric padding applied
method symmetric(source, direction, both_period, forward_period, backward_period)
Applies symmetric padding to an array by mirroring the data across boundaries
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with symmetric padding applied
reflect(source, series_length, direction, both_period, forward_period, backward_period)
Applies reflect padding by continuing trends through reflection around endpoint values
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with reflect padding applied
method reflect(source, direction, both_period, forward_period, backward_period)
Applies reflect padding to an array by continuing trends through reflection around endpoint values
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with reflect padding applied
periodic(source, series_length, direction, both_period, forward_period, backward_period)
Applies periodic padding by repeating the input data
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with periodic padding applied
method periodic(source, direction, both_period, forward_period, backward_period)
Applies periodic padding to an array by repeating the data
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with periodic padding applied
antisymmetric(source, series_length, direction, both_period, forward_period, backward_period)
Applies antisymmetric padding by mirroring data and alternating signs
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with antisymmetric padding applied
method antisymmetric(source, direction, both_period, forward_period, backward_period)
Applies antisymmetric padding to an array by mirroring data and alternating signs
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with antisymmetric padding applied
antireflect(source, series_length, direction, both_period, forward_period, backward_period)
Applies antireflect padding by reflecting around endpoints while preserving derivatives
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with antireflect padding applied
method antireflect(source, direction, both_period, forward_period, backward_period)
Applies antireflect padding to an array by reflecting around endpoints while preserving derivatives
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with antireflect padding applied. Note: Last data point is lost when using array input
smooth(source, series_length, direction, both_period, forward_period, backward_period)
Applies smooth padding by extending with constant derivatives from endpoints
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with smooth padding applied
method smooth(source, direction, both_period, forward_period, backward_period)
Applies smooth padding to an array by extending with constant derivatives from endpoints
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with smooth padding applied. Note: Last data point is lost when using array input
constant(source, series_length, direction, both_period, forward_period, backward_period)
Applies constant padding by extending endpoint values
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with constant padding applied
method constant(source, direction, both_period, forward_period, backward_period)
Applies constant padding to an array by extending endpoint values
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with constant padding applied
zero(source, series_length, direction, both_period, forward_period, backward_period)
Applies zero padding by extending with zeros
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with zero padding applied
method zero(source, direction, both_period, forward_period, backward_period)
Applies zero padding to an array by extending with zeros
Namespace types: array
Parameters:
source (array) : Array of values to pad
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with zero padding applied
pad_data(source, series_length, padding_type, direction, both_period, forward_period, backward_period)
Generic padding function that applies specified padding type to input data
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with specified padding applied
method pad_data(source, padding_type, direction, both_period, forward_period, backward_period)
Generic padding function that applies specified padding type to array input
Namespace types: array
Parameters:
source (array) : Array of values to pad
padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified
Returns: Array ordered with most recent point at index 0, containing original data with specified padding applied. Note: Last data point is lost when using antireflect or smooth padding types
make_padded_data(source, series_length, padding_type, direction, both_period, forward_period, backward_period)
Creates a window-based padded data series that updates with each new value. WARNING: Function must be called on every bar for consistency. Do not use in scopes where it may not execute on every bar.
Parameters:
source (float) : Input value to pad from
series_length (int) : Length of the data window
padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)
direction (series Direction) : Direction to apply padding
both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified
forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified
backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified
Returns: Array ordered with most recent point at index 0, containing windowed data with specified padding applied
Wavelet
Fine-tune Inputs: Fourier Smoothed Volume zone oscillator WFSVZ0Use this Strategy to Fine-tune inputs for the (W&)FSVZ0 Indicator.
Strategy allows you to fine-tune the indicator for 1 TimeFrame at a time; cross Timeframe Input fine-tuning is done manually after exporting the chart data.
I suggest using "Close all" input False when fine-tuning Inputs for 1 TimeFrame. When you export data to Excel/Numbers/GSheets I suggest using "Close all" input as True, except for the lowest TimeFrame.
MEANINGFUL DESCRIPTION:
The Volume Zone oscillator breaks up volume activity into positive and negative categories. It is positive when the current closing price is greater than the prior closing price and negative when it's lower than the prior closing price. The resulting curve plots through relative percentage levels that yield a series of buy and sell signals, depending on level and indicator direction.
The Wavelet & Fourier Smoothed Volume Zone Oscillator (W&)FSVZO is a refined version of the Volume Zone Oscillator, enhanced by the implementation of the Discrete Fourier Transform . Its primary function is to streamline price data and diminish market noise, thus offering a clearer and more precise reflection of price trends.
By combining the Wavalet and Fourier aproximation with Ehler's white noise histogram, users gain a comprehensive perspective on volume-related market conditions.
HOW TO USE THE INDICATOR:
The default period is 2 but can be adjusted after backtesting. (I suggest 5 VZO length and NoiceR max length 8 as-well)
The VZO points to a positive trend when it is rising above the 0% level, and a negative trend when it is falling below the 0% level. 0% level can be adjusted in setting by adjusting VzoDifference. Oscillations rising below 0% level or falling above 0% level result in a natural trend.
HOW TO USE THE STRATEGY:
Here you fine-tune the inputs until you find a combination that works well on all Timeframes you will use when creating your Automated Trade Algorithmic Strategy. I suggest 4h, 12h, 1D, 2D, 3D, 4D, 5D, 6D, W and M.
When I ndicator/Strategy returns 0 or natural trend , Strategy Closes All it's positions.
ORIGINALITY & USFULLNESS:
Personal combination of Fourier and Wavalet aproximation of a price which results in less noise Volume Zone Oscillator.
The Wavelet Transform is a powerful mathematical tool for signal analysis, particularly effective in analyzing signals with varying frequency or non-stationary characteristics. It dissects a signal into wavelets, small waves with varying frequency and limited duration, providing a multi-resolution analysis. This approach captures both frequency and location information, making it especially useful for detecting changes or anomalies in complex signals.
The Discrete Fourier Transform (DFT) is a mathematical technique that transforms discrete data from the time domain into its corresponding representation in the frequency domain. This process involves breaking down a signal into its individual frequency components, thereby exposing the amplitude and phase characteristics inherent in each frequency element.
This indicator utilizes the concept of Ehler's Universal Oscillator and displays a histogram, offering critical insights into the prevailing levels of market noise. The Ehler's Universal Oscillator is grounded in a statistical model that captures the erratic and unpredictable nature of market movements. Through the application of this principle, the histogram aids traders in pinpointing times when market volatility is either rising or subsiding.
DETAILED DESCRIPTION:
My detailed description of the indicator and use cases which I find very valuable.
What is oscillator?
Oscillators are chart indicators that can assist a trader in determining overbought or oversold conditions in ranging (non-trending) markets.
What is volume zone oscillator?
Price Zone Oscillator measures if the most recent closing price is above or below the preceding closing price.
Volume Zone Oscillator is Volume multiplied by the 1 or -1 depending on the difference of the preceding 2 close prices and smoothed with Exponential moving Average.
What does this mean?
If the VZO is above 0 and VZO is rising. We have a bullish trend. Most likely.
If the VZO is below 0 and VZO is falling. We have a bearish trend. Most likely.
Rising means that VZO on close is higher than the previous day.
Falling means that VZO on close is lower than the previous day.
What if VZO is falling above 0 line?
It means we have a high probability of a bearish trend.
Thus the indicator returns 0 and Strategy closes all it's positions when falling above 0 (or rising bellow 0) and we combine higher and lower timeframes to gauge the trend.
In the next Image you can see that trend is negative on 4h, negative on 12h and positive on 1D. That means trend is negative.
I am sorry, the chart is a bit messy. The idea is to use the indicator over more than 1 Timeframe.
What is approximation and smoothing?
They are mathematical concepts for making a discrete set of numbers a
continuous curved line.
Fourier and Wavelet approximation of a close price are taken from aprox library.
Key Features:
You can tailor the Indicator/Strategy to your preferences with adjustable parameters such as VZO length, noise reduction settings, and smoothing length.
Volume Zone Oscillator (VZO) shows market sentiment with the VZO, enhanced with Exponential Moving Average (EMA) smoothing for clearer trend identification.
Noise Reduction leverages Euler's White noise capabilities for effective noise reduction in the VZO, providing a cleaner and more accurate representation of market dynamics.
Choose between the traditional Fast Fourier Transform (FFT) , the innovative Double Discrete Fourier Transform (DTF32) and Wavelet soothed Fourier soothed price series to suit your analytical needs.
Image of Wavelet transform with FAST settings, Double Fourier transform with FAST settings. Improved noice reduction with SLOW settings, and standard FSVZO with SLOW settings:
Fast setting are setting by default:
VZO length = 2
NoiceR max Length = 2
Slow settings are:
VZO length = 5 or 7
NoiceR max Length = 8
As you can see fast setting are more volatile. I suggest averaging fast setting on 4h 12h 1d 2d 3d 4d W and M Timeframe to get a clear view on market trend.
What if I want long only when VZO is rising and above 15 not 0?
You have set Setting VzoDifference to 15. That reduces the number of trend changes.
Example of W&FSVZO with VzoDifference 15 than 0:
VZO crossed 0 line but not 15 line and that's why Indicator returns 0 in one case an 1 in another.
What is Smooth length setting?
A way of calculating Bullish or Bearish (W&)FSVZO .
If smooth length is 2 the trend is rising if:
rising = VZO > ta.ema(VZO, 2)
Meaning that we check if VZO is higher that exponential average of the last 2 elements.
If smooth length is 1 the trend is rising if:
rising = VZO_ > VZO_
Use this Strategy to fine-tune inputs for the (W&)FSVZO Indicator.
(Strategy allows you to fine-tune the indicator for 1 TimeFrame at a time; cross Timeframe Input fine-tuning is done manually after exporting the chart data)
I suggest using " Close all " input False when fine-tuning Inputs for 1 TimeFrame . When you export data to Excel/Numbers/GSheets I suggest using " Close all " input as True , except for the lowest TimeFrame . I suggest using 100% equity as your default quantity for fine-tune purposes. I have to mention that 100% equity may lead to unrealistic backtesting results. Be avare. When backtesting for trading purposes use Contracts or USDT.
Wavelet & Fourier Smoothed Volume zone oscillator (W&)FSVZO Indicator id:
USER;e7a774913c1242c3b1354334a8ea0f3c
(only relevant to those that use API requests)
MEANINGFUL DESCRIPTION:
The Volume Zone oscillator breaks up volume activity into positive and negative categories. It is positive when the current closing price is greater than the prior closing price and negative when it's lower than the prior closing price. The resulting curve plots through relative percentage levels that yield a series of buy and sell signals, depending on level and indicator direction.
The Wavelet & Fourier Smoothed Volume Zone Oscillator (W&)FSVZO is a refined version of the Volume Zone Oscillator, enhanced by the implementation of the Discrete Fourier Transform. Its primary function is to streamline price data and diminish market noise, thus offering a clearer and more precise reflection of price trends.
By combining the Wavalet and Fourier aproximation with Ehler's white noise histogram, users gain a comprehensive perspective on volume-related market conditions.
HOW TO USE THE INDICATOR:
The default period is 2 but can be adjusted after backtesting. (I suggest 5 VZO length and NoiceR max length 8 as-well)
The VZO points to a positive trend when it is rising above the 0% level, and a negative trend when it is falling below the 0% level. 0% level can be adjusted in setting by adjusting VzoDifference. Oscillations rising below 0% level or falling above 0% level result in natural trend.
ORIGINALITY & USFULLNESS:
Personal combination of Fourier and Wavalet aproximation of a price which results in less noise Volume Zone Oscillator.
The Wavelet Transform is a powerful mathematical tool for signal analysis, particularly effective in analyzing signals with varying frequency or non-stationary characteristics. It dissects a signal into wavelets, small waves with varying frequency and limited duration, providing a multi-resolution analysis. This approach captures both frequency and location information, making it especially useful for detecting changes or anomalies in complex signals.
The Discrete Fourier Transform (DFT) is a mathematical technique that transforms discrete data from the time domain into its corresponding representation in the frequency domain. This process involves breaking down a signal into its individual frequency components, thereby exposing the amplitude and phase characteristics inherent in each frequency element.
This indicator utilizes the concept of Ehler's Universal Oscillator and displays a histogram, offering critical insights into the prevailing levels of market noise. The Ehler's Universal Oscillator is grounded in a statistical model that captures the erratic and unpredictable nature of market movements. Through the application of this principle, the histogram aids traders in pinpointing times when market volatility is either rising or subsiding.
DETAILED DESCRIPTION:
My detailed description of the indicator and use cases which I find very valuable.
What is oscillator?
Oscillators are chart indicators that can assist a trader in determining overbought or oversold conditions in ranging (non-trending) markets.
What is volume zone oscillator?
Price Zone Oscillator measures if the most recent closing price is above or below the preceding closing price.
Volume Zone Oscillator is Volume multiplied by the 1 or -1 depending on the difference of the preceding 2 close prices and smoothed with Exponential moving Average.
What does this mean?
If the VZO is above 0 and VZO is rising. We have a bullish trend. Most likely.
If the VZO is below 0 and VZO is falling. We have a bearish trend. Most likely.
Rising means that VZO on close is higher than the previous day.
Falling means that VZO on close is lower than the previous day.
What if VZO is falling above 0 line?
It means we have a high probability of a bearish trend.
Thus the indicator returns 0 when falling above 0 (or rising bellow 0) and we combine higher and lower timeframes to gauge the trend.
In the next Image you can see that trend is positive on 4h, neutral on 12h and positive on 1D. That means trend is positive.
I am sorry, the chart is a bit messy. The idea is to use the indicator over more than 1 Timeframe.
What is approximation and smoothing?
They are mathematical concepts for making a discrete set of numbers a
continuous curved line.
Fourier and Wavelet approximation of a close price are taken from aprox library.
Key Features:
You can tailor the indicator to your preferences with adjustable parameters such as VZO length, noise reduction settings, and smoothing length.
Volume Zone Oscillator (VZO) shows market sentiment with the VZO, enhanced with Exponential Moving Average (EMA) smoothing for clearer trend identification.
Noise Reduction leverages Euler's White noise capabilities for effective noise reduction in the VZO, providing a cleaner and more accurate representation of market dynamics.
Choose between the traditional Fast Fourier Transform (FFT), the innovative Double Discrete Fourier Transform (DTF32) and Wavelet soothed Fourier soothed price series to suit your analytical needs.
Image of Wavelet transform with FAST settings, Double Fourier transform with FAST settings. Improved noice reduction with SLOW settings, and standard FSVZO with SLOW settings:
Fast setting are setting by default:
VZO length = 2
NoiceR max Length = 2
Slow settings are:
VZO length = 5 or 7
NoiceR max Length = 8
As you can see fast setting are more volatile. I suggest averaging fast setting on 4h 12h 1d 2d 3d 4d W and M Timeframe to get a clear view on market trend.
What if I want long only when VZO is rising and above 15 not 0?
You have set Setting VzoDifference to 15. That reduces the number of trend changes.
Example of W&FSVZO with VzoDifference 15 than 0:
VZO crossed 0 line but not 15 line and that's why Indicator returns 0 in one case an 1 in another.
What is Smooth length setting?
A way of calculating Bullish or Bearish FSVZO.
If smooth length is 2 the trend is rising if:
rising = VZO > ta.ema(VZO, 2)
Meaning that we check if VZO is higher that exponential average of the last 2 elements.
If smooth length is 1 the trend is rising if:
rising = VZO_ > VZO_
Rising is boolean value, meaning TRUE if rising and FALSE if falling.
Mathematical equations presented in Pinescript:
Fourier of the real (x axis) discrete:
x_0 = array.get(x, 0) + array.get(x, 1) + array.get(x, 2)
x_1 = array.get(x, 0) + array.get(x, 1) * math.cos( -2 * math.pi * _dir / 3 ) - array.get(y, 1) * math.sin( -2 * math.pi * _dir / 3 ) + array.get(x, 2) * math.cos( -4 * math.pi * _dir / 3 ) - array.get(y, 2) * math.sin( -4 * math.pi * _dir / 3 )
x_2 = array.get(x, 0) + array.get(x, 1) * math.cos( -4 * math.pi * _dir / 3 ) - array.get(y, 1) * math.sin( -4 * math.pi * _dir / 3 ) + array.get(x, 2) * math.cos( -8 * math.pi * _dir / 3 ) - array.get(y, 2) * math.sin( -8 * math.pi * _dir / 3 )
Euler's Noice reduction with both close and Discrete Furrier approximated price.
w = (dft1*src - dft1 *src ) / math.sqrt(math.pow(math.abs(src- src ),2) + math.pow(math.abs(dft1 - dft1 ),2))
filt := na(filt ) ? 0 : c1 * (w*dft1 + nz(w *dft1 )) / 2.0 /math.abs(dft1 -dft1 ) + c2 * nz(filt ) - c3 * nz(filt )
Usecase:
First option:
Select the preferred version of DFT and noise reduction settings based on your analysis requirements.
Leverage the script to identify Bullish and Bearish trends, shown with green and red triangle.
Combine Different Timeframes to accurately determine market trend.
Second option:
Pull the data with API sockets to automate your trading journey.
plot(close, title="ClosePrice", display=display.status_line)
plot(open, title="OpenPrice", display=display.status_line)
plot(greencon ? 1 : redcon ? -1 : 0, title="position", display=display.status_line)
Use ClosePrice, OpenPrice and "position" titles to easily read and backtest your strategy utilising more than 1 Time Frame.
Indicator id:
USER;e7a774913c1242c3b1354334a8ea0f3c
(only relevant to those that use API requests)
