PINE LIBRARY
NormalizedOscillators
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Library "NormalizedOscillators"
Collection of some common Oscillators. All are zero-mean and normalized to fit in the -1..1 range. Some are modified, so that the internal smoothing function could be configurable (for example, to enable Hann Windowing, that John F. Ehlers uses frequently). Some are modified for other reasons (see comments in the code), but never without a reason. This collection is neither encyclopaedic, nor reference, however I try to find the most correct implementation. Suggestions are welcome.
rsi2(upper, lower) RSI - second step
Parameters:
upper: Upwards momentum
lower: Downwards momentum
Returns: Oscillator value
Modified by Ehlers from Wilder's implementation to have a zero mean (oscillator from -1 to +1)
Originally: 100.0 - (100.0 / (1.0 + upper / lower))
Ignoring the 100 scale factor, we get: upper / (upper + lower)
Multiplying by two and subtracting 1, we get: (2 * upper) / (upper + lower) - 1 = (upper - lower) / (upper + lower)
rms(src, len) Root mean square (RMS)
Parameters:
src: Source series
len: Lookback period
Based on by John F. Ehlers implementation
ift(src) Inverse Fisher Transform
Parameters:
src: Source series
Returns: Normalized series
Based on by John F. Ehlers implementation
The input values have been multiplied by 2 (was "2*src", now "4*src") to force expansion - not compression
The inputs may be further modified, if needed
stoch(src, len) Stochastic
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
ssstoch(src, len) Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Introduced in the January 2014 issue of Stocks and Commodities
This is not an implementation of MESA Stochastic, as it is based on Highpass filter not present in the function (but you can construct it)
This implementation is scaled by 0.95, so that Super Smoother does not exceed 1/-1
I do not know, if this the right way to fix this issue, but it works for now
netKendall(src, len) Noise Elimination Technology by John F. Ehlers
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Introduced in the December 2020 issue of Stocks and Commodities
Uses simplified Kendall correlation algorithm
Implementation by QuantTherapy:
rsi(src, len, smooth) RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
vrsi(src, len, smooth) Volume-scaled RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
This is my own version of RSI. It scales price movements by the proportion of RMS of volume
mrsi(src, len, smooth) Momentum RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
rrsi(src, len, smooth) Rocket RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
Does not include Fisher Transform of the original implementation, as the output must be normalized
Does not include momentum smoothing length configuration, so always assumes half the lookback length
mfi(src, len, smooth) Money Flow Index
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
lrsi(src, in_gamma, len) Laguerre RSI by John F. Ehlers
Parameters:
src: Source series
in_gamma: Damping factor (default is -1 to generate from len)
len: Lookback period (alternatively, if gamma is not set)
Returns: Oscillator series
The original implementation is with gamma. As it is impossible to collect gamma in my system, where the only user input is length,
an alternative calculation is included, where gamma is set by dividing len by 30. Maybe different calculation would be better?
fe(len) Choppiness Index or Fractal Energy
Parameters:
len: Lookback period
Returns: Oscillator series
The Choppiness Index (CHOP) was created by E. W. Dreiss
This indicator is sometimes called Fractal Energy
er(src, len) Efficiency ratio
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Based on Kaufman Adaptive Moving Average calculation
This is the correct Efficiency ratio calculation, and most other implementations are wrong:
the number of bar differences is 1 less than the length, otherwise we are adding the change outside of the measured range!
For reference, see Stocks and Commodities June 1995
dmi(len, smooth) Directional Movement Index
Parameters:
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Based on the original Tradingview algorithm
Modified with inspiration from John F. Ehlers DMH (but not implementing the DMH algorithm!)
Only ADX is returned
Rescaled to fit -1 to +1
Unlike most oscillators, there is no src parameter as DMI works directly with high and low values
fdmi(len, smooth) Fast Directional Movement Index
Parameters:
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Same as DMI, but without secondary smoothing. Can be smoothed later. Instead, +DM and -DM smoothing can be configured
doOsc(type, src, len, smooth) Execute a particular Oscillator from the list
Parameters:
type: Oscillator type to use
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Chande Momentum Oscillator (CMO) is RSI without smoothing. No idea, why some authors use different calculations
LRSI with Fractal Energy is a combo oscillator that uses Fractal Energy to tune LRSI gamma, as seen here: prorealcode.com/prorealtime-indicators/rsi-laguerre-adjusting-gamma-fractals-energy/
doPostfilter(type, src, len) Execute a particular Oscillator Postfilter from the list
Parameters:
type: Oscillator type to use
src: Source series
len: Lookback period
Returns: Oscillator series
Collection of some common Oscillators. All are zero-mean and normalized to fit in the -1..1 range. Some are modified, so that the internal smoothing function could be configurable (for example, to enable Hann Windowing, that John F. Ehlers uses frequently). Some are modified for other reasons (see comments in the code), but never without a reason. This collection is neither encyclopaedic, nor reference, however I try to find the most correct implementation. Suggestions are welcome.
rsi2(upper, lower) RSI - second step
Parameters:
upper: Upwards momentum
lower: Downwards momentum
Returns: Oscillator value
Modified by Ehlers from Wilder's implementation to have a zero mean (oscillator from -1 to +1)
Originally: 100.0 - (100.0 / (1.0 + upper / lower))
Ignoring the 100 scale factor, we get: upper / (upper + lower)
Multiplying by two and subtracting 1, we get: (2 * upper) / (upper + lower) - 1 = (upper - lower) / (upper + lower)
rms(src, len) Root mean square (RMS)
Parameters:
src: Source series
len: Lookback period
Based on by John F. Ehlers implementation
ift(src) Inverse Fisher Transform
Parameters:
src: Source series
Returns: Normalized series
Based on by John F. Ehlers implementation
The input values have been multiplied by 2 (was "2*src", now "4*src") to force expansion - not compression
The inputs may be further modified, if needed
stoch(src, len) Stochastic
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
ssstoch(src, len) Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Introduced in the January 2014 issue of Stocks and Commodities
This is not an implementation of MESA Stochastic, as it is based on Highpass filter not present in the function (but you can construct it)
This implementation is scaled by 0.95, so that Super Smoother does not exceed 1/-1
I do not know, if this the right way to fix this issue, but it works for now
netKendall(src, len) Noise Elimination Technology by John F. Ehlers
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Introduced in the December 2020 issue of Stocks and Commodities
Uses simplified Kendall correlation algorithm
Implementation by QuantTherapy:
rsi(src, len, smooth) RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
vrsi(src, len, smooth) Volume-scaled RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
This is my own version of RSI. It scales price movements by the proportion of RMS of volume
mrsi(src, len, smooth) Momentum RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
rrsi(src, len, smooth) Rocket RSI
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
Does not include Fisher Transform of the original implementation, as the output must be normalized
Does not include momentum smoothing length configuration, so always assumes half the lookback length
mfi(src, len, smooth) Money Flow Index
Parameters:
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
lrsi(src, in_gamma, len) Laguerre RSI by John F. Ehlers
Parameters:
src: Source series
in_gamma: Damping factor (default is -1 to generate from len)
len: Lookback period (alternatively, if gamma is not set)
Returns: Oscillator series
The original implementation is with gamma. As it is impossible to collect gamma in my system, where the only user input is length,
an alternative calculation is included, where gamma is set by dividing len by 30. Maybe different calculation would be better?
fe(len) Choppiness Index or Fractal Energy
Parameters:
len: Lookback period
Returns: Oscillator series
The Choppiness Index (CHOP) was created by E. W. Dreiss
This indicator is sometimes called Fractal Energy
er(src, len) Efficiency ratio
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Based on Kaufman Adaptive Moving Average calculation
This is the correct Efficiency ratio calculation, and most other implementations are wrong:
the number of bar differences is 1 less than the length, otherwise we are adding the change outside of the measured range!
For reference, see Stocks and Commodities June 1995
dmi(len, smooth) Directional Movement Index
Parameters:
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Based on the original Tradingview algorithm
Modified with inspiration from John F. Ehlers DMH (but not implementing the DMH algorithm!)
Only ADX is returned
Rescaled to fit -1 to +1
Unlike most oscillators, there is no src parameter as DMI works directly with high and low values
fdmi(len, smooth) Fast Directional Movement Index
Parameters:
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Same as DMI, but without secondary smoothing. Can be smoothed later. Instead, +DM and -DM smoothing can be configured
doOsc(type, src, len, smooth) Execute a particular Oscillator from the list
Parameters:
type: Oscillator type to use
src: Source series
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Chande Momentum Oscillator (CMO) is RSI without smoothing. No idea, why some authors use different calculations
LRSI with Fractal Energy is a combo oscillator that uses Fractal Energy to tune LRSI gamma, as seen here: prorealcode.com/prorealtime-indicators/rsi-laguerre-adjusting-gamma-fractals-energy/
doPostfilter(type, src, len) Execute a particular Oscillator Postfilter from the list
Parameters:
type: Oscillator type to use
src: Source series
len: Lookback period
Returns: Oscillator series
Note di rilascio
v2 - Added:momentum(src, len) Momentum
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Derivative of the oscillator series with IFT normalization to force the -1..1 range
Note di rilascio
v3 Added:avx(len, smooth) Average Vortex Index (AVX)
Parameters:
len: Lookback period
smooth: Internal smoothing algorithm
Returns: Oscillator series
Based on the Vortex Indicator. I then apply ADX calculation on the VI+ and VI- lines.
Only AVX is returned
Rescaled to fit -1 to +1
Unlike most oscillators, there is no src parameter as AVX works directly with high and low values
Note di rilascio
v4 Added "Fast Default" internal smoothing algorithm: same as Default, but with half the lengthNote di rilascio
v5 Added:hurst(src, len) Hurst Exponent
Parameters:
src: Source series
len: Lookback period
Returns: Oscillator series
Until I can write my own, I use the nolantait library:
Which in turn is based on the excellent balipour implementation:
![Hurst Exponent - Detrended Fluctuation Analysis [pig]](https://s3.tradingview.com/v/vTloluai_mid.png)
As with all other indicators, this is also rescaled to fit -1 to +1
Note di rilascio
v6 Added:fd(len) Simple Fractal Dimension
Parameters:
len: Reference lookback length
Returns: Oscillator series
Based on FRAMA by John F. Ehlers
This function implements just the first part of FRAMA: calculating Fractal Dimension
It is then transformed to Hurst Exponent (HE = 2 - FD) and normalized to fit -1 to +1
Note di rilascio
v7 Added:fve(len) Finite Volume Element (FVE)
Parameters:
len: Lookback period
Returns: Oscillator series
Based on FVE with Volatility adjustment by Markos Katsanos (Stocks and Commodities, September 2003)
Note di rilascio
v8 Added:vfi(len) Volume Flow Indicator (VFI)
Parameters:
len: Lookback period
Returns: Oscillator series
Based on VFI by Markos Katsanos (Stocks and Commodities, June 2004)
mkatsanos.com/volume-flow-vfi-indicator/
As with all other indicators, this is also rescaled to fit -1 to +1
Note di rilascio
v9 Added:rvi(len) Relative Vigor Index by John F. Ehlers
Parameters:
len: Lookback period
Returns: Oscillator series
Introduced in the January 2002 issue of Stocks and Commodities
Similar to A/D Oscillator
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