Enhanced WaveTrend OscillatorThe Enhanced WaveTrend Oscillator is a modified version of the original WaveTrend. The WaveTrend indicator is a popular technical analysis tool used to identify overbought and oversold conditions in the market and generate trading signals. The enhanced version addresses certain limitations of the original indicator and introduces additional features for improved analysis and comparison across assets.
WaveTrend:
The original WaveTrend indicator calculates two lines based on exponential moving averages and their relationship to the asset's price. The first line measures the distance between the asset's price and its EMA, while the second line smooths the first line over a specific period. The result is divided by 0.015 multiplied by the smoothed difference ('d' for reference). The indicator aims to identify overbought and oversold conditions by analyzing the relationship between the two lines.
In the original formula, the rudimentary estimation factor 0.015 times 'd' fails to accomodate for approximately a quarter of the data, preventing the indicator from reaching the traditional stationary levels of +-100. This limitation renders the indicator quantitatively biased, as it relies on the user's subjective adjustment of the levels. The enhanced version replaces this factor with the standard deviation of the asset's price, resulting in improved estimation accuracy and provides a more dynamic and robust outcome, we thereafter multiply the result by 100 to achieve a more traditional oscillation.
Enhancements and Features:
The enhanced version of the WaveTrend indicator addresses several limitations of the original indicator and introduces additional features-
Dynamic Estimation: The original indicator uses an arbitrary estimation factor, while the enhanced version replaces it with the standard deviation of the asset's price. This modification provides a more dynamic and accurate estimation, adapting to the specific price characteristics of each asset.
Stationary Support and Resistance Levels: The enhanced version provides stationary key support and resistance levels that range from -150 to 150. These levels are determined based on the analysis of the indicator's data and encompass more than 95% of the indicator's values. These levels offer important reference points for traders to identify potential price reversals or significant price movements.
Comparison Across Assets: The enhanced version allows for better comparison and analysis across different assets. By incorporating the standard deviation of the asset's price, the indicator provides a more consistent and comparable interpretation of the market conditions across multiple assets.
Upon closer inspection of the modification in the enhanced version, we can observe that the resulting indicator is a smoothed variation of the Z-Score!
f_ewave(src, chlen, avglen) =>
basis = ta.ema(src, chlen)
dev = ta.stdev(src, chlen)
wave = (src - basis) / dev * 100
ta.ema(wave, avglen)
Z-Score Analysis:
The Z-Score is a statistical measurement that quantifies how far a particular data point deviates from the mean in terms of standard deviations. In the enhanced version, the calculation involves determining the basis (mean) and deviation (standard deviation) of the asset's price to calculate its Z-Score, thereafter applying a smoothing technique to generate the final WaveTrend value.
Utility:
The 𝗘𝗻𝗵𝗮𝗻𝗰𝗲𝗱 𝗪𝗧 indicator offers traders and investors valuable insights into overbought and oversold conditions in the market. By analyzing the indicator's values and referencing the stationary support and resistance levels, traders can identify potential trend reversals, evaluate market strength, and make better informed analysis.
It is important to note that this indicator should be used in conjunction with other technical analysis tools and indicators to confirm trading signals and validate market dynamics.
Credit:
The 𝗘𝗻𝗵𝗮𝗻𝗰𝗲𝗱 𝗪𝗧 indicator is a modification of the original WaveTrend Oscillator developed by @LazyBear on TradingView.
Example Charts:
Wavetrendoscillator
WaveTrend 3D█ OVERVIEW
WaveTrend 3D (WT3D) is a novel implementation of the famous WaveTrend (WT) indicator and has been completely redesigned from the ground up to address some of the inherent shortcomings associated with the traditional WT algorithm.
█ BACKGROUND
The WaveTrend (WT) indicator has become a widely popular tool for traders in recent years. WT was first ported to PineScript in 2014 by the user @LazyBear, and since then, it has ascended to become one of the Top 5 most popular scripts on TradingView.
The WT algorithm appears to have origins in a lesser-known proprietary algorithm called Trading Channel Index (TCI), created by AIQ Systems in 1986 as an integral part of their commercial software suite, TradingExpert Pro. The software’s reference manual states that “TCI identifies changes in price direction” and is “an adaptation of Donald R. Lambert’s Commodity Channel Index (CCI)”, which was introduced to the world six years earlier in 1980. Interestingly, a vestige of this early beginning can still be seen in the source code of LazyBear’s script, where the final EMA calculation is stored in an intermediate variable called “tci” in the code.
█ IMPLEMENTATION DETAILS
WaveTrend 3D is an alternative implementation of WaveTrend that directly addresses some of the known shortcomings of the indicator, including its unbounded extremes, susceptibility to whipsaw, and lack of insight into other timeframes.
In the canonical WT approach, an exponential moving average (EMA) for a given lookback window is used to assess the variability between price and two other EMAs relative to a second lookback window. Since the difference between the average price and its associated EMA is essentially unbounded, an arbitrary scaling factor of 0.015 is typically applied as a crude form of rescaling but still fails to capture 20-30% of values between the range of -100 to 100. Additionally, the trigger signal for the final EMA (i.e., TCI) crossover-based oscillator is a four-bar simple moving average (SMA), which further contributes to the net lag accumulated by the consecutive EMA calculations in the previous steps.
The core idea behind WT3D is to replace the EMA-based crossover system with modern Digital Signal Processing techniques. By assuming that price action adheres approximately to a Gaussian distribution, it is possible to sidestep the scaling nightmare associated with unbounded price differentials of the original WaveTrend method by focusing instead on the alteration of the underlying Probability Distribution Function (PDF) of the input series. Furthermore, using a signal processing filter such as a Butterworth Filter, we can eliminate the need for consecutive exponential moving averages along with the associated lag they bring.
Ideally, it is convenient to have the resulting probability distribution oscillate between the values of -1 and 1, with the zero line serving as a median. With this objective in mind, it is possible to borrow a common technique from the field of Machine Learning that uses a sigmoid-like activation function to transform our data set of interest. One such function is the hyperbolic tangent function (tanh), which is often used as an activation function in the hidden layers of neural networks due to its unique property of ensuring the values stay between -1 and 1. By taking the first-order derivative of our input series and normalizing it using the quadratic mean, the tanh function performs a high-quality redistribution of the input signal into the desired range of -1 to 1. Finally, using a dual-pole filter such as the Butterworth Filter popularized by John Ehlers, excessive market noise can be filtered out, leaving behind a crisp moving average with minimal lag.
Furthermore, WT3D expands upon the original functionality of WT by providing:
First-class support for multi-timeframe (MTF) analysis
Kernel-based regression for trend reversal confirmation
Various options for signal smoothing and transformation
A unique mode for visualizing an input series as a symmetrical, three-dimensional waveform useful for pattern identification and cycle-related analysis
█ SETTINGS
This is a summary of the settings used in the script listed in roughly the order in which they appear. By default, all default colors are from Google's TensorFlow framework and are considered to be colorblind safe.
Source: The input series. Usually, it is the close or average price, but it can be any series.
Use Mirror: Whether to display a mirror image of the source series; for visualizing the series as a 3D waveform similar to a soundwave.
Use EMA: Whether to use an exponential moving average of the input series.
EMA Length: The length of the exponential moving average.
Use COG: Whether to use the center of gravity of the input series.
COG Length: The length of the center of gravity.
Speed to Emphasize: The target speed to emphasize.
Width: The width of the emphasized line.
Display Kernel Moving Average: Whether to display the kernel moving average of the signal. Like PCA, an unsupervised Machine Learning technique whereby neighboring vectors are projected onto the Principal Component.
Display Kernel Signal: Whether to display the kernel estimator for the emphasized line. Like the Kernel MA, it can show underlying shifts in bias within a more significant trend by the colors reflected on the ribbon itself.
Show Oscillator Lines: Whether to show the oscillator lines.
Offset: The offset of the emphasized oscillator plots.
Fast Length: The length scale factor for the fast oscillator.
Fast Smoothing: The smoothing scale factor for the fast oscillator.
Normal Length: The length scale factor for the normal oscillator.
Normal Smoothing: The smoothing scale factor for the normal frequency.
Slow Length: The length scale factor for the slow oscillator.
Slow Smoothing: The smoothing scale factor for the slow frequency.
Divergence Threshold: The number of bars for the divergence to be considered significant.
Trigger Wave Percent Size: How big the current wave should be relative to the previous wave.
Background Area Transparency Factor: Transparency factor for the background area.
Foreground Area Transparency Factor: Transparency factor for the foreground area.
Background Line Transparency Factor: Transparency factor for the background line.
Foreground Line Transparency Factor: Transparency factor for the foreground line.
Custom Transparency: Transparency of the custom colors.
Total Gradient Steps: The maximum amount of steps supported for a gradient calculation is 256.
Fast Bullish Color: The color of the fast bullish line.
Normal Bullish Color: The color of the normal bullish line.
Slow Bullish Color: The color of the slow bullish line.
Fast Bearish Color: The color of the fast bearish line.
Normal Bearish Color: The color of the normal bearish line.
Slow Bearish Color: The color of the slow bearish line.
Bullish Divergence Signals: The color of the bullish divergence signals.
Bearish Divergence Signals: The color of the bearish divergence signals.
█ ACKNOWLEDGEMENTS
@LazyBear - For authoring the original WaveTrend port on TradingView
@PineCoders - For the beautiful color gradient framework used in this indicator
@veryfid - For the inspiration of using mirrored signals for cycle analysis and using multiple lookback windows as proxies for other timeframes
+ WaveTrend Oscillator OverlayAn overlay version of pertinent signals from my version of LazyBear's Wavetrend Oscillator.
Shows momentum of long period WTO as either background colors or symbols.
Shows continuation and reversal trade signals.
If Secondary WTO is above the center line (momentum is long), then symbols print across the top of the chart when the primary (faster) WTO comes into "oversold," a number associated with a horizontal line on the off-chart indicator. This number is selectable via a drop-down menu. Same thing for bearish momentum.
Conversely, reversal signals are printed along the bottom when conditions are met. Ex: if the Secondary WTO is showing momentum is bullish, then symbols will print along the bottom when the primary WTO is at "overbought" (or whatever number you deem overbought--again, via a similar drop-down menu).
Also, symbols are printed above and below candles for when the moving average of the primary WTO is crossed.
You could use these for taking profits, exiting a trade, or entering a trade.
Includes a moving average that is an average of the 200 EMA, SMA and Kijun.
Alerts.
Enjoy.
//p.s. I recommend using this in conjunction with my "+ Wavetrend Oscillator" at least starting out. Helps to have a visual
//reference when picking reversal and continuation numbers.
+ WaveTrend OscillatorI'm guessing most of you are familir with LazyBear's adaptation of the Wavetrend Oscillator; it's one of the most popular indicators on TradingView. I know others have done adaptations of it, but I thought I might as well, because that's kind of a thing I like doing.
In this version I've added a second Wavetrend plot. This is a thing I like to do. The longer plot gives you a longer timeframe momentum bias, and the shorter plot gives you entries and/or exits. Here we have one plot with a lookback period of 55, and another with the default set to 6 (change this to 14 if you think you might prefer something slower and that will plot similarly to the default RSI settings). With the traditional Wavetrend Oscillator there is a simple moving average on the WTO that is to help provide entries and exits. I've done away with this as there are already two plots, and I felt more would just clutter the indicator. Instead of plotting the SMA I've plotted the crosses along the bottom and top of the indicator. Also, as is not the case in LazyBear's version, this SMA length is adjustable. By default it is set to 3, which is the default setting on the original indicator.
I've also plotted background colors for when there is what I call a momentum shift. If one or the other oscillators crosses the centerline a colored bar is plotted. By default it is turned on for both WTOs, though in practice you might only want it on for the longer one.
I would say use of the indicator is similar to the original WTO or many other oscillators. Buying oversold and selling overbought, but being mindful of the momentum of the market. If the longer WTO is above the centerline it's best to be looking for dips to the centerline, or for an overbought signal by the faster WTO, and vice versa if the longer WTO is below the centerline. That said, you can also adjust the length of the SMA on the faster WTO to fine tune entries or exits, which is kind of how you would trade LazyBear's version. In this case you have that additional confirmation of market momentum.
You can set colored candles to either of the WTO plots via a dropdown menu.
There are alerts for overbought and oversold situations, centerline crosses, and Wavetrend crosses.
That's about it. Hope you enjoy this particular implementation of LazyBear's well known indicator.
Ah yes, last thing: Original version the source is set to hlc3. I've given you the opportunity to change that, so if you prefer using close you can, or whatever you want.
