Differences in p-value results from an Augmented Dickey-Fuller (ADF) test between Python and MATLAB could arise from several factors:
1. Implementation Differences: Python's statsmodels and MATLAB's adftest might use slightly different algorithms or criteria for the ADF test.
2. Test Assumptions: The ADF test in both Python and MATLAB make assumptions about the data and the test, including assumptions about the presence of a unit root, the presence of a drift term or a deterministic time trend, and so forth. If the assumptions are not met, it can lead to different results.
3. Different Levels of Significance: Python and MATLAB may use different levels of significance, which could lead to different p-value interpretations.
4. Sample Size: The number of observations used for the test can significantly impact the p-value. Ensure that both Python and MATLAB are working with the same dataset size.
5. Lag Length Selection: The choice of maximum lags in the ADF regression could be different in Python and MATLAB, causing differences in the outcome.
6. Data Preprocessing: Ensure that your data preprocessing steps are the same across both platforms.
If you're getting significantly different p-values, I'd recommend reviewing the test parameters and the implementation details in both Python and MATLAB, ensuring that you're comparing like-for-like in terms of data, assumptions, and the statistical test itself. If the differences persist, it might be helpful to seek advice from a statistician or someone familiar with the specific nuances of these testing methods in Python and MATLAB.
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