GKD-C Lyapunov Hodrick-Prescott Oscillator w/ DSL [Loxx]

26. März 2023

Giga Kaleidoscope GKD-C Lyapunov Hodrick-Prescott Oscillator w/ DSL is a Confirmation module included in Loxx's "Giga Kaleidoscope Modularized Trading System".

█ Giga Kaleidoscope Modularized Trading System

What is Loxx's "Giga Kaleidoscope Modularized Trading System"?
The Giga Kaleidoscope Modularized Trading System is a trading system built on the philosophy of the NNFX (No Nonsense Forex) algorithmic trading.

What is the NNFX algorithmic trading strategy?
The NNFX (No-Nonsense Forex) trading system is a comprehensive approach to Forex trading that is designed to simplify the process and remove the confusion and complexity that often surrounds trading. The system was developed by a Forex trader who goes by the pseudonym "VP" and has gained a significant following in the Forex community.

The NNFX trading system is based on a set of rules and guidelines that help traders make objective and informed decisions. These rules cover all aspects of trading, including market analysis, trade entry, stop loss placement, and trade management.

Here are the main components of the NNFX trading system:

1. Trading Philosophy: The NNFX trading system is based on the idea that successful trading requires a comprehensive understanding of the market, objective analysis, and strict risk management. The system aims to remove subjective elements from trading and focuses on objective rules and guidelines.

2. Technical Analysis: The NNFX trading system relies heavily on technical analysis and uses a range of indicators to identify high-probability trading opportunities. The system uses a combination of trend-following and mean-reverting strategies to identify trades.

3. Market Structure: The NNFX trading system emphasizes the importance of understanding the market structure, including price action, support and resistance levels, and market cycles. The system uses a range of tools to identify the market structure, including trend lines, channels, and moving averages.

4. Trade Entry: The NNFX trading system has strict rules for trade entry. The system uses a combination of technical indicators to identify high-probability trades, and traders must meet specific criteria to enter a trade.

5. Stop Loss Placement: The NNFX trading system places a significant emphasis on risk management and requires traders to place a stop loss order on every trade. The system uses a combination of technical analysis and market structure to determine the appropriate stop loss level.

6. Trade Management: The NNFX trading system has specific rules for managing open trades. The system aims to minimize risk and maximize profit by using a combination of trailing stops, take profit levels, and position sizing.

Overall, the NNFX trading system is designed to be a straightforward and easy-to-follow approach to Forex trading that can be applied by traders of all skill levels.

Core components of an NNFX algorithmic trading strategy
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:

1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted

What is Volatility in the NNFX trading system?
In the NNFX (No Nonsense Forex) trading system, ATR (Average True Range) is typically used to measure the volatility of an asset. It is used as a part of the system to help determine the appropriate stop loss and take profit levels for a trade. ATR is calculated by taking the average of the true range values over a specified period.

True range is calculated as the maximum of the following values:

-Current high minus the current low
-Absolute value of the current high minus the previous close
-Absolute value of the current low minus the previous close

ATR is a dynamic indicator that changes with changes in volatility. As volatility increases, the value of ATR increases, and as volatility decreases, the value of ATR decreases. By using ATR in NNFX system, traders can adjust their stop loss and take profit levels according to the volatility of the asset being traded. This helps to ensure that the trade is given enough room to move, while also minimizing potential losses.

Other types of volatility include True Range Double (TRD), Close-to-Close, and Garman-Klass

What is a Baseline indicator?
The baseline is essentially a moving average, and is used to determine the overall direction of the market.

The baseline in the NNFX system is used to filter out trades that are not in line with the long-term trend of the market. The baseline is plotted on the chart along with other indicators, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR).

Trades are only taken when the price is in the same direction as the baseline. For example, if the baseline is sloping upwards, only long trades are taken, and if the baseline is sloping downwards, only short trades are taken. This approach helps to ensure that trades are in line with the overall trend of the market, and reduces the risk of entering trades that are likely to fail.

By using a baseline in the NNFX system, traders can have a clear reference point for determining the overall trend of the market, and can make more informed trading decisions. The baseline helps to filter out noise and false signals, and ensures that trades are taken in the direction of the long-term trend.

What is a Confirmation indicator?
Confirmation indicators are technical indicators that are used to confirm the signals generated by primary indicators. Primary indicators are the core indicators used in the NNFX system, such as the Average True Range (ATR), the Moving Average (MA), and the Relative Strength Index (RSI).

The purpose of the confirmation indicators is to reduce false signals and improve the accuracy of the trading system. They are designed to confirm the signals generated by the primary indicators by providing additional information about the strength and direction of the trend.

Some examples of confirmation indicators that may be used in the NNFX system include the Bollinger Bands, the MACD (Moving Average Convergence Divergence), and the Stochastic Oscillator. These indicators can provide information about the volatility, momentum, and trend strength of the market, and can be used to confirm the signals generated by the primary indicators.

In the NNFX system, confirmation indicators are used in combination with primary indicators and other filters to create a trading system that is robust and reliable. By using multiple indicators to confirm trading signals, the system aims to reduce the risk of false signals and improve the overall profitability of the trades.

What is a Continuation indicator?
In the NNFX (No Nonsense Forex) trading system, a continuation indicator is a technical indicator that is used to confirm a current trend and predict that the trend is likely to continue in the same direction. A continuation indicator is typically used in conjunction with other indicators in the system, such as a baseline indicator, to provide a comprehensive trading strategy.

What is a Volatility/Volume indicator?
Volume indicators, such as the On Balance Volume (OBV), the Chaikin Money Flow (CMF), or the Volume Price Trend (VPT), are used to measure the amount of buying and selling activity in a market. They are based on the trading volume of the market, and can provide information about the strength of the trend. In the NNFX system, volume indicators are used to confirm trading signals generated by the Moving Average and the Relative Strength Index. Volatility indicators include Average Direction Index, Waddah Attar, and Volatility Ratio. In the NNFX trading system, volatility is a proxy for volume and vice versa.

By using volume indicators as confirmation tools, the NNFX trading system aims to reduce the risk of false signals and improve the overall profitability of trades. These indicators can provide additional information about the market that is not captured by the primary indicators, and can help traders to make more informed trading decisions. In addition, volume indicators can be used to identify potential changes in market trends and to confirm the strength of price movements.

What is an Exit indicator?
The exit indicator is used in conjunction with other indicators in the system, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR), to provide a comprehensive trading strategy.

The exit indicator in the NNFX system can be any technical indicator that is deemed effective at identifying optimal exit points. Examples of exit indicators that are commonly used include the Parabolic SAR, the Average Directional Index (ADX), and the Chandelier Exit.

The purpose of the exit indicator is to identify when a trend is likely to reverse or when the market conditions have changed, signaling the need to exit a trade. By using an exit indicator, traders can manage their risk and prevent significant losses.

In the NNFX system, the exit indicator is used in conjunction with a stop loss and a take profit order to maximize profits and minimize losses. The stop loss order is used to limit the amount of loss that can be incurred if the trade goes against the trader, while the take profit order is used to lock in profits when the trade is moving in the trader's favor.

Overall, the use of an exit indicator in the NNFX trading system is an important component of a comprehensive trading strategy. It allows traders to manage their risk effectively and improve the profitability of their trades by exiting at the right time.

How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v1.0 system has five types of modules (indicators/strategies). These modules are:

1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)

(additional module types will added in future releases)

Each module interacts with every module by passing data between modules. Data is passed between each module as described below:

GKD-B => GKD-V => GKD-C(1) => GKD-C(2) => GKD-C(Continuation) => GKD-E => GKD-BT

That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.

This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.

What does the application of the GKD trading system look like?
Example trading system:

• Backtest: Strategy with 1-3 take profits, trailing stop loss, multiple types of PnL volatility, and 2 backtesting styles
  
• Baseline: Hull Moving Average
  
• Volatility/Volume: Hurst Exponent
  
• Confirmation 1: Lyapunov Hodrick-Prescott Oscillator w/ DSL as shown on the chart above
  
• Confirmation 2: Williams Percent Range
  
• Continuation: Fisher Transform
  
• Exit: Rex Oscillator
  

Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD protocol chain.

Giga Kaleidoscope Modularized Trading System Signals (based on the NNFX algorithm)
Standard Entry
1. GKD-C Confirmation 1 Signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees

Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior

Continuation Entry
1. Standard Entry, Baseline Entry, or Pullback; entry triggered previously
2. GKD-B Baseline hasn't crossed since entry signal trigger
3. GKD-C Confirmation Continuation Indicator signals
4. GKD-C Confirmation 1 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 2 agrees

1-Candle Rule Standard Entry
1. GKD-C Confirmation 1 signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
Next Candle:
1. Price retraced (Long: close < close[1] or Short: close > close[1])
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees

1-Candle Rule Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close[1] or Short: close > close[1])
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees

PullBack Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is beyond 1.0x Volatility of Baseline
Next Candle:
1. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees

█ GKD-C Lyapunov Hodrick-Prescott Oscillator w/ DSL

What is Hodrick–Prescott filter?
The Hodrick-Prescott (HP) filter is a mathematical tool used in macroeconomics to separate a time series into its trend component and its cyclical component. It was developed by economists Robert Hodrick and Edward Prescott in 1980.

The HP filter works by decomposing a time series into two components: a trend component and a cyclical component. The trend component represents the long-term behavior of the time series, while the cyclical component represents the short-term fluctuations around the trend.

The HP filter is based on the assumption that the trend component of a time series varies smoothly over time, while the cyclical component varies more rapidly. The filter uses a mathematical algorithm to estimate the trend component of the time series, and then subtracts the trend from the original time series to obtain the cyclical component.

The HP filter is widely used in macroeconomics to analyze business cycles, as it allows researchers to separate the underlying trend in economic data from the short-term fluctuations. It is also used in finance to analyze asset prices, and in other fields where time series analysis is important.

What is Lyapunov stability?
Lyapunov stability is a concept in control theory and dynamical systems theory that concerns the stability of a system or a point in the system's state space. Specifically, it is a method for analyzing the behavior of nonlinear systems in terms of their asymptotic stability.

The basic idea behind Lyapunov stability is to consider a function, called a Lyapunov function, that measures the distance between the system's current state and some reference state, and then use this function to determine whether the system is stable or unstable. In particular, a system is said to be Lyapunov stable if, for any initial condition within some region around the reference state, the system's trajectory will eventually converge to the reference state as time goes to infinity.

A Lyapunov function must satisfy certain conditions to be useful for analyzing stability, such as being positive definite and decreasing along the trajectories of the system. Lyapunov stability is often used to analyze the stability of equilibrium points, which are states where the system's behavior does not change over time.

Chaos theory is a branch of mathematics that studies the behavior of dynamic systems that are highly sensitive to initial conditions. It is used to study systems that exhibit complex and seemingly random behavior over time. Chaos theory is closely related to the study of nonlinear dynamical systems, which are systems that do not exhibit the linearity property, which means that their behavior is not proportional to their inputs.

One of the key tools of chaos theory is the Lyapunov exponent, which is a measure of the rate at which nearby trajectories in a dynamic system diverge over time. In chaotic systems, the Lyapunov exponent is positive, indicating that small differences in initial conditions lead to exponentially divergent trajectories over time.

Chaos theory has applications in a wide range of fields, including physics, engineering, biology, economics, and finance. It provides a powerful tool for understanding the behavior of complex systems, and is often used to model the behavior of natural systems such as weather patterns, fluid dynamics, and ecological systems.

What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.

Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.

"Signal" line is calculated the following way :

When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level

This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.

In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.

What is Lyapunov Hodrick-Prescott Oscillator w/ DSL?
Lyapunov Hodrick-Prescott Oscillator w/ DSL is a Hodrick-Prescott Channel Filter that is modified using the Lyapunov stability algorithm to turn the filter into an oscillator. Signals are created using Discontinued Signal Lines or Zero-line crosses.

Requirements
Inputs
Confirmation 1 and Solo Confirmation: GKD-V Volatility / Volume indicator
Confirmation 2: GKD-C Confirmation indicator

Outputs
Confirmation 2 and Solo Confirmation Complex: GKD-E Exit indicator
Confirmation 1: GKD-C Confirmation indicator
Continuation: GKD-E Exit indicator
Solo Confirmation Simple: GKD-BT Backtest strategy

Additional features will be added in future releases.

13. Apr. 2023

Versionshinweise

Upgraded to relax signal rules. This only applies to the Full GKD systems. All settings for signals are controlled by the Confirmation 2 indicator. So this means when you build a Full GKD system, the C2 indicator controls the relaxation of all signals including the Continuation indicator that you are required to add on top of the C2 indicator the full GKD system.

Added the following signal types:
Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior

1-Candle Rule Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close)
2. GKD-B Volatility/Volume agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees

Added the following backtest options
-Super Complex allows for the creation of a GKD system without Confirmation 2 indicator. This backtest type requires the addition of a GKD-C Confirmation indicator
-Stacked allows for the creation of infinitely stackable GKD-C indicators. This is useful for combining two GKD-C indicators to test their synergy together before using these indicators in a full GKD system.

14. Apr. 2023

Versionshinweise

Updated to handle GKD-V stacks

15. Apr. 2023

Versionshinweise

Added volatility signals to continuation signal qualifiers.

Added Confirmation 1 + Confirmation 2 backtesting. This allows you to backtest C1 with C2 indicators together without setting up the full GKD system. In the GKD system, the C2 indicator acts as a minor trend filter while the C1 indicator delivers the actual signals and entries. This new backtest allows you to test the entries and signals from the C1 indicator while using the C2 indicator as the macrotrend filter.

7. Mai 2023

Versionshinweise

Updated for new GKD backtests.

12. Mai 2023

Versionshinweise

Additions and Subtractions:

-All signal logic has been transferred to the new GKD-BT Backtests. You can access these backtests using the links provided below:

GKD-BT Giga Confirmation Stack Backtest:

GKD-BT Giga Stacks Backtest:

GKD-BT Full Giga Kaleidoscope Backtest:

GKD-BT Solo Confirmation Super Complex Backtest:

GKD-BT Solo Confirmation Complex Backtest:

GKD-BT Solo Confirmation Simple Backtest:

-Removed all Confirmation Type options except for "Confirmation" and "Continuation." The "Continuation" type is only used in GKD-BT Solo Confirmation Super Complex Backtest and GKD-BT Full Giga Kaleidoscope Backtest when selecting a Confirmation indicator.

-Added new signal plots based on the selected Confirmation Type. For the "Confirmation" type, only initial Longs and Shorts will be displayed on the indicator. For the "Continuation" type, both initial and continuation signals will be displayed. In both cases, if multiple signal types are present (e.g., middle cross, signal cross), these signals can be controlled using the "Signal Type" option.

-Implemented code optimizations to enhance the rendering speed of signals.

-Streamlined the export process by generating only a single value for export to other indicators or backtests. This exported value is named "Input into NEW GKD-BT Backtest."

1. Juni 2023

Versionshinweise

Updated for multi-ticker backtests

5. Juni 2023

Versionshinweise

increased speed

27. Juni 2023

Versionshinweise

Updated for gkd optimizers.