A tool for automatic sequence analysis

[Dmitry]

Hello everyone,
I am working on a Python tool for automatic sequence analysis and would like to share it with the community. Its goal is to identify the underlying structure of a sequence by applying a wide range of analyses.
GitHub Repository: https://github.com/FekDN/SequenceAnalyzer
The tool is open source, and I would be very grateful for your expert feedback. I am particularly interested in:
 - Sequences where the current analysis fails or gives incorrect results.
 - Suggestions for new types of analysis that would be valuable for OEIS contributors.
Thank you.

[Tomas Rokicki]

Does it do Berlekamp-Massey, for instance?

-tom

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[Dmitry]

The analyzer doesn't use the Berlekamp-Massey algorithm directly.

For finding linear recurrences, it currently uses a statistical approach: it fits autoregressive models of different orders using least squares and selects the best one based on the Akaike Information Criterion.

BM is an algebraic method that's perfect for finding the exact minimal recurrence for a sequence, while my current approach is more of a statistical best-fit that's robust to noise or slight deviations from a perfect recurrence.

Adding Berlekamp-Massey is an excellent suggestion for a future improvement. Thank you for pointing it out!

пн, 27 окт. 2025 г., 21:59 Tomas Rokicki <rok...@gmail.com>:

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[Antti Karttunen]

Thanks, interesting!

I wonder what are the minimal amounts of terms you recommend for some of those analyzes?

Also, I suggest that you add a small function like https://github.com/karttu/OEIS-Djinn/blob/master/src/OEIS-Djinn-on-stripped.py#L808

to your program, so to make it easier to run it on the b-files.

Best regards,

Antti

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[Dmitry]

Thank you, that's an excellent question! I'll add this information to
the project description.

The analyzer uses a variety of methods, each with its own data
requirements. Generally, the more complex the pattern a method seeks,
the more data it needs to produce a reliable result.

Here is a brief guide to the recommended minimum sequence lengths for
different types of analysis:

1. Foundational Metrics (5-15+ terms):
Functions: local_dynamics (5), statistical_moments (2),
dependency_model (polynomials, 5-10), anomalies (4).
Why: This is enough data to calculate basic moments (mean,
variance), derivatives (velocity, acceleration), and fit simple
curves. These concepts are not meaningful on fewer points.

2. Core Time Series Analysis (20-40+ terms):
Functions: stationarity (20), cyclicity_and_seasonality (approx.
20-30), entropy_analysis (20), spectral_analysis (20),
structural_breaks (20), complexity_analysis (20),
stream_structure_analysis (30), state_segmentation (HMM, ~36).
Why: These methods need sufficient data to establish a
"statistical regime." Stationarity tests must distinguish trends from
noise, cycle detection needs to see at least one or two full periods,
and HMM needs enough samples to learn the characteristics of each
hidden state.

3. Advanced & Structural Analysis (50+ terms):
Functions: nonlinear_fractal_analysis (Hurst/DFA, 50),
volatility_analysis (GARCH, 50), empirical_mode_decomposition (50),
hybrid_model_analysis (50).
Why: These methods model more complex properties. GARCH analyzes
the volatility of returns, fractal analysis investigates
self-similarity and scaling properties, and EMD decomposes the signal
into nested oscillatory modes—all of which require a longer data
history to be reliable.

4. Highly Demanding (Chaos & Attractor) Analysis (100+ terms):
Functions: nonlinear_fractal_analysis (Correlation
Dimension/Lyapunov Exponent, 100).
Why: These methods attempt to reconstruct a system's attractor in
phase space from a single time series. This is an extremely
data-hungry task, and results on shorter sequences would be
statistically insignificant.

In general, longer sequences yield more reliable and insightful
results, especially for the advanced methods.

пн, 27 окт. 2025 г. в 18:03, Antti Karttunen <antti.k...@gmail.com>:

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