Bitcoin Price Prediction using Machine Learning and Combinatorial Fusion Analysis

This paper proposes a Bitcoin price prediction model using Combinatorial Fusion Analysis (CFA) to integrate diverse machine learning models via rank-score characteristics and weighted combinations, achieving a superior Mean Absolute Percentage Error (MAPE) of 0.19% that outperforms individual models and existing prediction methods.

The Gist

Imagine you are trying to guess the price of Bitcoin tomorrow. It's like trying to predict the weather, but instead of rain or sunshine, the "weather" is a wildly unpredictable digital currency that can swing up or down by thousands of dollars in a single day.

This paper is about a team of researchers who decided to stop relying on just one "weather forecaster" and instead built a super-team of forecasters to get the best possible prediction.

Here is the story of how they did it, broken down into simple steps:

1. The Problem: One Expert Isn't Enough

In the past, people tried to predict Bitcoin prices using single computer programs (Machine Learning models). Think of these models as individual experts:

• The Statistician: Good at spotting patterns in numbers.
• The Neural Network: Good at remembering long-term history.
• The Tree-Planter: Good at making decisions based on "if this, then that" rules.

The problem is that every expert has blind spots. Sometimes the Statistician is right, but the Neural Network is wrong. Sometimes the Tree-Planter is confused by a sudden market crash. Relying on just one is risky.

2. The Solution: The "Super-Team" (Combinatorial Fusion Analysis)

The researchers used a method called Combinatorial Fusion Analysis (CFA). Imagine you are a judge on a talent show. Instead of listening to just one judge, you have five.

• Judge A gives a score of 8/10.
• Judge B gives a score of 9/10.
• Judge C thinks it's a 6/10.

Instead of just averaging their scores, CFA looks at how different their opinions are. If all five judges agree, it's a safe bet. But if they disagree, CFA uses a special math trick to figure out which judge is usually the most reliable in that specific situation and combines their votes in a way that cancels out the mistakes.

3. The Ingredients: What Did They Feed the Team?

To make the predictions, they didn't just look at Bitcoin's past price. They fed the team a massive "smoothie" of data, including:

• The Crypto Cousins: The price of Ethereum (ETH) and Gold.
• The Miners' Power: How much computing power is being used to secure Bitcoin (Hashrate).
• The Global Mood: The S&P 500 (stock market), the VIX (fear index), and even the price of Tesla and Nvidia (because Elon Musk and computer chips affect crypto).
• The "Secret Sauce": They also added technical math tools that look at trends, like moving averages.

4. The Secret Sauce: Not Just a Number, But a "Cloud"

Most prediction models try to guess a single number (e.g., "Bitcoin will be $95,000"). The researchers thought, "That's too rigid."

Instead, they asked each of their 5 models to draw a cloud of possibilities.

• Model A says: "It's probably around $95k, but could be between $90k and $100k."
• Model B says: "It's probably $94k, but could be between $92k and $96k."

They then used their "Super-Team" math to merge these clouds. Where the clouds overlap the most is where the true price is likely to be. This is like looking at a group of people throwing darts at a board; the spot where the most darts cluster is your best guess.

5. The Result: A Crystal Ball That Actually Works

They tested this method on data from 2020 to 2024. The results were impressive:

• The Error Rate: Their method was off by only 0.19% on average.
• The Comparison: Other famous methods in the past had error rates of 0.39%, 1.33%, or even 4.49%.

The Analogy:
If you were betting on the price of Bitcoin, using an old method is like asking a friend to guess the temperature. They might say "It's 70 degrees," but they could be off by 10 degrees.
Using this new method is like asking a team of meteorologists, checking their radar, their satellite data, and their historical records, and then combining their reports to say, "It's 70 degrees, and we are 99% sure it's between 69.5 and 70.5."

Why Does This Matter?

The paper proves that diversity is strength. By combining models that think differently (some are good at short-term trends, some at long-term history) and using a smart way to mix their opinions, you get a prediction that is much more robust and accurate than any single model could ever be alone.

In short: They didn't just build a better crystal ball; they built a crystal ball that listens to five different voices and knows how to ignore the noise to find the truth.

Technical Summary

Here is a detailed technical summary of the paper "Bitcoin Price Prediction using Machine Learning and Combinatorial Fusion Analysis."

1. Problem Statement

The paper addresses the challenge of predicting the daily price of Bitcoin, a highly volatile financial asset. While numerous machine learning (ML) models exist for this task (e.g., ARIMA, LSTM, Random Forest), individual models often suffer from specific weaknesses, such as overfitting, inability to capture long-term dependencies, or poor performance during extreme market volatility. The authors argue that relying on a single model limits robustness and accuracy. The goal is to develop a superior prediction framework that leverages the complementary strengths of diverse models to minimize error metrics like Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE).

2. Methodology

The proposed methodology utilizes Combinatorial Fusion Analysis (CFA), a paradigm that combines multiple scoring systems using rank-score characteristic (RSC) functions and cognitive diversity. The workflow consists of four distinct phases:

A. Data Preparation

• Dataset: Daily data from March 11, 2020, to March 9, 2024 (covering the post-COVID-19 pandemic period).
• Features: Includes Bitcoin price, Ethereum (ETH) price, Gold price, Hashrate, S&P 500, VIX Index, US bond yield, Dollar Strength, Nvidia price, and Tesla price. Technical indicators like EMA and MACD are also incorporated.
• Preprocessing: Missing values (due to weekend trading differences) are forward-filled. Data is normalized to the range [0, 1]. The dataset is split 80:20 into training and testing sets.

B. Base Models

Five diverse base models are employed to generate initial predictions:

1. SVM (Support Vector Machine): For regression tasks.
2. Random Forest (RF): An ensemble of decision trees.
3. XGBoost: Gradient boosting framework.
4. CNN (Convolutional Neural Network): 1D convolutional layers to detect localized patterns.
5. LSTM (Long Short-Term Memory): To capture long-term temporal dependencies.
   Note: Models are optimized using 10-fold cross-validation and random search.

C. Prediction Distribution Generation (Phase II)

Instead of predicting a single deterministic value, the authors generate a normal distribution for each day's prediction for every model:

• Mean: The predicted price from the model.
• Standard Deviation: Derived from the original test set's error variability (assumed stable for a given model).
• Truncation: Distributions are truncated at $\pm 2$ standard deviations to capture ~95% of the price range.
• Scoring Systems: The probabilities derived from these distributions serve as "scores," and the price intervals serve as "data items," creating five distinct scoring systems.

D. Combinatorial Fusion Analysis (Phase III & IV)

The core innovation lies in fusing these five systems:

1. Grouping: All possible subsets of the 5 models are created (pairs, triplets, etc.), resulting in 26 unique model groups.
2. Combination Strategies: Four strategies are applied to these groups:
   • Average Score Combination (AC-SC)
   • Average Rank Combination (AC-RC)
   • Weighted Score Combination by Diversity Strength (WCDS-SC)
   • Weighted Rank Combination by Diversity Strength (WCDS-RC)
   • Weighting Logic: Weights are assigned based on Cognitive Diversity (CD), calculated via the distance between Rank-Score Characteristic (RSC) functions. High diversity implies models make different errors, which is beneficial for fusion.
3. Selection: For each day, the model combination yielding the highest probability (lowest absolute distance to the actual price) is selected as the final prediction.

3. Key Contributions

• Novel Application of CFA: This is the first study to apply Combinatorial Fusion Analysis specifically to Bitcoin next-day price prediction.
• Distribution-Based Prediction: Moving beyond point estimates, the method generates price distributions, allowing for a probabilistic approach to fusion.
• Cognitive Diversity Utilization: The framework explicitly quantifies and utilizes the "dissimilarity" between models (via RSC functions) to weight combinations, rather than relying solely on individual model accuracy.
• Comprehensive Benchmarking: The study compares the proposed method against both individual base models and a wide array of state-of-the-art literature.

4. Results

The performance was evaluated on a 292-day test set using RMSE and MAPE.

• Individual vs. Combined: All combination methods significantly outperformed individual base models.
  • Best Individual Model (SVM): RMSE = 738.21, MAPE = 1.20%.
  • Best Combined Model (Average Score Combination): RMSE = 175.22, MAPE = 0.19%.
• Metric Comparison:
  • RMSE: Score-based combinations generally achieved lower RMSE values than rank-based ones.
  • MAPE: The Average Score Combination (AC-SC) achieved a MAPE of 0.19%, which is approximately 10 times better than the best individual model and significantly lower than previous studies.
• Comparison with State-of-the-Art:
  • The proposed method (0.19% MAPE) outperforms advanced ensemble models from recent literature (e.g., VMD-AGRU-RESVMD-LSTM at 0.394%, GRU at 0.245%, and DNN at 3.61%).
• Improvement Frequency: The weighted rank combination by diversity strength showed improved accuracy over the baseline on 258 out of 292 days (88% of the time).

5. Significance

• Robustness: The study demonstrates that fusing diverse models via CFA creates a more robust predictor that is less susceptible to the specific failure modes of individual algorithms.
• Superior Accuracy: Achieving a 0.19% MAPE sets a new benchmark for daily Bitcoin price prediction, suggesting that the "wisdom of crowds" (via algorithmic fusion) is highly effective in volatile financial markets.
• Theoretical Insight: The results validate the hypothesis that cognitive diversity is a critical factor in ensemble learning; models that behave differently (high CD) complement each other better than models that are merely accurate but similar.
• Future Directions: The authors suggest incorporating consumer sentiment analysis and exploring multi-layer CFA frameworks to further refine predictions, while noting a limitation regarding the use of test-set standard deviation (potential data leakage) for future correction.