The purpose of this article is to help readers understand how to engage in long-term, stable trading based on legitimate trading theories through orthodox quantitative analysis trading strategies. We hope that you can increase the success rate and stability of your trades through scientific methods and rigorous analysis. Note: If you are looking for quick profits of several percentage points daily or doubling your money in a few days, and you start by asking about rates of return, please look elsewhere. Those unwilling to learn, your knowledge determines your mind and your wallet.
I. Introduction
Based on the first article that explained what pair trading is, this article aims to analyze the cointegration relationship between Bitcoin (BTC) and Ethereum (ETH) to determine if they are suitable for pair trading.
Cointegration, the primary element of pair trading, let's explain the theory.
In this image, the distance between the little girl (Type A) and the dog (Type B) vividly describes the cointegration relationship in pair trading.
Just like the girl walking her dog, even though the leash allows the dog some freedom of movement, the dog is ultimately constrained by the leash and cannot stray too far from the girl. This reflects the cointegration relationship between two assets in pair trading: although their prices may fluctuate in the short term, they maintain a certain synchronized relationship over the long term, much like the leash keeping the dog close to the girl. This relationship ensures that regardless of the walking path, the distance between them stays within a bounded range, symbolizing the stability sought in pair trading arbitrage opportunities.
II. Cointegration Analysis
We first used two methods to test the cointegration relationship between BTC and ETH: validating the cointegration relationship is the most critical step for pair trading, as it helps you select more stable, potentially profitable asset pairs, reduce trading risk, and improve trading success rates.
It can be simply understood as two assets having a common price movement trend over the long term. Even though their prices may fluctuate in the short term, their price differences will stabilize over the long term.
1. Engle-Granger Two-Step Method The Engle-Granger two-step method is used to detect whether there is a cointegration relationship between BTC and ETH. This method involves two steps:
Regression Analysis: Conduct linear regression analysis on the prices of BTC and ETH to calculate their residuals.
Stationarity Test: Perform an Augmented Dickey-Fuller (ADF) test on the residuals to determine if they are stationary. If the residuals are stationary, it indicates that the two have a common movement trend in the long term.
Results:
ADF Test Statistic: -2.6849
p-value: 0.0751
Critical Values: 1% -3.430, 5% -2.862, 10% -2.567
At the 5% significance level, the ADF test statistic fails to be less than the 5% critical value, and thus we cannot confirm that the residuals are stationary, making it impossible to confirm a stable cointegration relationship between BTC and ETH in the long term.
2. Johansen Cointegration Test We used the Johansen cointegration test to further validate the cointegration relationship between BTC and ETH.
Results:
The first test statistic: 14.918756, critical values: 90% - 13.4294, 95% - 15.4943, 99% - 19.9349
The second test statistic: 3.466325, critical values: 90% - 2.7055, 95% - 3.8415, 99% - 6.6349
At the 90% confidence level, the first test statistic is greater than the 90% critical value, and the second test statistic is also greater than the 90% critical value, indicating the existence of a cointegration relationship between BTC and ETH.
III. Differences in Methods
The different results of the Engle-Granger two-step method and the Johansen test are due to their differing testing methods and applicable conditions.
Engle-Granger Two-Step Method:
Single-equation method: Handles the relationship between two variables at a time.
Dependent on the accuracy of the regression model: If the regression model is inaccurate, the results may also be inaccurate.
Sensitive to data preprocessing: If the data is not well processed, the results may be biased.
Johansen Test:
Multi-equation method: Can handle multiple time series relationships simultaneously.
Vector Autoregression Model (VAR): Uses more complex models to determine cointegration relationships.
High statistical power: Especially in large samples, it can more accurately detect cointegration relationships.
Therefore, the Engle-Granger two-step method may produce unstable results due to sample size or data characteristics, whereas the Johansen test is more robust and can provide accurate results in more complex situations.
IV. Correlation Analysis
To further verify the price relationship between BTC and ETH, we performed correlation coefficient and lagged correlation analysis.
1. Correlation Coefficient Calculation
Result: The correlation coefficient is 0.918, indicating a strong positive correlation between the two.
2. Lagged Correlation Analysis
We analyzed the lagged correlation from 1 hour to 24 hours to determine the impact of BTC price changes on ETH price.
Result: At 1-hour lag, the correlation is very high, close to 0.92. As the lag time increases, the correlation gradually decreases but remains at a high level. At 24-hour lag, the correlation is 0.914.
V. Linear Regression Model Analysis
We constructed a linear regression model, using BTC price as the independent variable and ETH price as the dependent variable, to analyze the relationship between the two.
Result: Regression Equation: ETH price = 0.0592 × BTC price - 46.57. The model results indicate that BTC price can explain most of the variations in ETH price, with a good fit for the model.
VI. Comprehensive Summary
Although the Engle-Granger two-step method did not significantly confirm the cointegration relationship between BTC and ETH, the Johansen test indicated a cointegration relationship in the long term. Additionally, the correlation analysis and linear regression model further validated the strong correlation and price linkage between BTC and ETH. Therefore, it is theoretically possible to consider BTC and ETH for pair trading, designing short-term pair trading strategy models while cautiously engaging in long-term pair trading.
VII. Suitability for Strategy Model Development
Considering that the volatility of the crypto market is much higher than traditional currency markets, intense price fluctuations of BTC and ETH may increase the risk of pair trading. In conditions of low liquidity, short-term trade execution may be affected, leading to increased slippage. This pair trading carries high risk.
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