Discussing the article: "How to Use Finite Differences for Price Forecasting"

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Check out the new article: How to Use Finite Differences for Price Forecasting.

The article examines the practical application of finite differences in trading: types of differences, their relationship to price dynamics, and the binomial transform for noise filtering. The rules for encoding patterns based on difference levels and the application of these patterns to forecasting are described. This section presents naive, adaptive, and probabilistic approaches that help smooth time series, identify recurring patterns, and estimate future movements.

Finite differences are a numerical method for estimating the derivative of a function using the function's values at discrete points. By using them, a trader can analyze changes in an asset's price over time, identify patterns, trends, and potential entry and exit points for positions.

Although finite differences have been known for a very long time, they are not used very often in trading. In this article, we will explore the application of finite differences in trading, starting with the basic concepts and ending with practical examples of their use. The main purpose of this article is to introduce traders to the finite difference method and show how it can be used to make more informed trading decisions.

In this article, we will examine various types of finite differences—forward and central finite differences. Let's discuss their advantages and disadvantages, and also examine how finite differences can be used for data smoothing, noise filtering, and forecasting.


Author: Aleksej Poljakov

 

Probabilistic Forecast.mq5

Criticisms and limitations:

  1. Assumption of independence: The code multiplies the probabilities of the differences as if they were independent. In reality, $D^{(1)}$ and $D^{(2)}$ are strongly correlated. This introduces a slight bias.

  2. Discreteness: The price in the code is converted to int (points). During sharp price movements, the histogram may become ‘blurred’.

  3. Memory: The indicator remembers ‘everything’. But the market changes. I would recommend adding a forgetting factor for old data.
    4. After a few minutes, the indicator’s levels shoot up on the EURUSD H1 chart.
    The indicator is recursively feeding itself! The array swells, the probabilities spread out in a thin layer (becoming uniform), and the expected value shoots off to infinity. That’s when your arrows fly off to the moon.

Trading recommendations

  1. Entry point (Buy): The price has touched the red line (price_dn), whilst the green line (price_me) is pointing upwards.

  2. Exit point: The price touches the blue line (price_up).

  3. Capital management: Use Bernoulli’s moral expectation. If price_me is significantly above the current price, and the risk ratio (distance to price_dn versus distance to price_up) > 1.5, the trade is rational.

Verdict: This is an excellent example of a ‘non-indicator’ approach. It attempts to model the probability density of the future price. I would call it the ‘Statistical Prophet for the Poor’.

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