Market Misfit: Adaptive Filters

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The previous article has already led us into the world of John F. Ehlers' theory, delving into the definitions and conversions of high-pass filters, low-pass filters, band-pass filters, and band-stop filters. But do you know? There is another type of filter that does not belong to these four types, and it is the adaptive filter! Today, let's briefly talk about this alternative!

The adaptive filter is like a chameleon in the market, it can automatically adjust its parameters according to market changes. Just like in the world of cats, we can adjust our behavior automatically according to environmental changes, isn't that impressive?

This type of filter can automatically adjust its filtering effect based on market volatility and periodicity. When the market trend is obvious, it can reduce the filtering effect, allowing us to better capture the power of the trend. And when the market is oscillating, it can increase the filtering effect, helping us filter out some noise. Just like in the world of cats, we can adjust our behavior based on environmental changes to better adapt to our surroundings.

The emergence of adaptive filters provides us with a more flexible and intelligent tool to better understand and analyze the dynamics of the market. Just like in the world of cats, we can adjust our behavior based on environmental changes to become smarter and more clever.

The key characteristic of adaptive filters is that their parameters or structures can be dynamically adjusted based on input data, just like chameleons in the market that change with market fluctuations. They can react more sensitively to current market conditions, just like how we adjust our expressions based on the taste of food while eating, very flexible, right?

For example, Ehlers' MESA Adaptive Moving Average (MAMA) is an adaptive filter. It dynamically adjusts the smoothing parameters based on the inherent cyclicality of market prices. So, when the market prices exhibit strong periodicity, MAMA will be closer to the prices, while it will be smoother when the periodicity of prices is weaker. It's like adjusting our expressions based on the taste of food while savoring it, making ourselves more sensitive and adaptable.

In John F. Ehlers' approach, adaptive filters are based on dynamically adjusting their parameters or structures based on market data. Therefore, they are somewhat unique and not strictly classified as traditional low-pass, high-pass, or band-pass filters.

The adaptive technical indicators developed by John F. Ehlers include:

MESA Adaptive Moving Average (MAMA)

Adaptive Laguerre Filter

Variable Index Dynamic Average (VIDYA)

Better Sinewave (although its purpose is to identify market cycles, its calculation method has adaptive characteristics)

Inverse Fisher Transform (used in combination with Decycler, with adaptive characteristics)

Generalized DEMA (sometimes considered to have adaptive characteristics)

These adaptive filters and indicators can better adapt to market changes and provide more timely and accurate signals, especially when market conditions change.

Usually, constructing an adaptive filter involves the following elements:

Period Measurement: To make the filter adaptive, it is first necessary to determine the dominant cycles in the price data. Ehlers provides various methods to estimate these cycles, such as Hilbert Transform or Homodyne Discriminator.

Dynamic Adjustment of Smoothing Coefficients: Use the information obtained from the period measurement to dynamically adjust the smoothing parameters or coefficients of the filter.

Basic Structure of the Filter: Select a basic filter, such as Exponential Moving Average (EMA), and apply it using the dynamically adjusted parameters.

Ensuring Boundaries: When implementing adaptive techniques, ensure the stability of the algorithm and the effective range of parameters.

To construct a completely new adaptive filter, you can follow these steps:

Data Analysis: Analyze your data first to determine its inherent cyclic characteristics or other features you want to capture.

Select a Basic Filter: Choose a basic filter as a starting point, it can be a simple moving average, exponential moving average, or any other filter.

Define Adaptive Algorithm: Design an algorithm to dynamically adjust the parameters of the filter. This is usually based on the analysis of data periodicity, but other market features can also be considered.

Testing: Test your adaptive filter on historical data to ensure it works stably under different market conditions.

Optimization and Adjustment: Adjust your filter based on the test results to optimize its performance.

Implementation in Actual Trading: Once you are satisfied with the filter, you can start using it in actual trading, but it is better to test it in a simulated environment first.

Therefore, constructing an adaptive filter requires in-depth analysis of market data, understanding its dynamic nature, and using this knowledge to dynamically adjust the parameters of the filter. Ehlers' work provides many useful tools and frameworks to assist in this analysis.

Many of John F. Ehlers' research and methods focus on utilizing digital signal processing techniques to extract and analyze cyclical components in the market, resulting in more effective and faster-responding technical indicators. Combining the content of previous articles, it can be summarized that there are two types of technical indicators that may be very useful in the market:

Traditional Oscillators: These are band-pass filters composed of traditional low-pass and high-pass filters (or other methods), such as RSI, Stochastic, and various oscillators created based on JFE theory.

Adaptive Oscillators: These are created based on adaptive filtering techniques and can adjust their parameters according to the dynamic conditions of the market. Ehlers' MESA Adaptive Moving Average (MAMA) and other related methods are examples of such oscillators.

Furthermore, adaptive technology is the key to John F. Ehlers' approach. Traditional technical indicators often use fixed parameters, which may perform well under certain market conditions but not in others. By using adaptive methods, indicators can better follow the market, reduce lag, and remain effective in different market environments. The core of this strategy is to use band-pass filters, whether based on traditional methods or adaptive technology. These filters aim to capture some kind of cycle or frequency in the market, seeking to provide valuable signals.