[foreswater]

LLM generated content, by GPT-6

What does this implement/fix? Explain your changes.

ANM Lec 2's time-domain features notebook lacks a runnable example of self-similarity and the Hurst exponent. This change appends a short explanation and a NumPy/Matplotlib example to lectures/lec2/Time_Domain_Features.ipynb.

The example generates a fractional Brownian motion path with a fixed seed and H=0.75, estimates H from the log-log scaling of increment standard deviations, and plots the simulated path and fitted scaling relationship. The explanation distinguishes H from a self-similarity score and limits this estimator's interpretation to fBm-like paths.

Does your contribution introduce a new dependency? If yes, which one?

No. The example uses NumPy and Matplotlib, which are already used in the notebook.

What should a reviewer concentrate their feedback on?

The clarity of the self-similarity explanation, the interpretation of H for fBm increments, and the suitability of the example for ANM Lec 2.

Did you add any tests for the change?

No new automated test files were added for this teaching example. Validation performed:

• Validated the prepared notebook with nbformat.validate.
• Executed the added code cell locally with Python 3.12.14, NumPy 2.3.5, and Matplotlib 3.11.2. Output: True H: 0.75; Estimated H: 0.765 (unrounded estimate: 0.7647405450609949).
• Visually checked the generated time-series and log-log plots.
• Confirmed the existing 13 notebook cells are unchanged; the diff only appends the two teaching cells.

The full notebook installation cell and Google Colab runtime were not re-tested for this change.

PR checklist

• The PR title starts with [DOC].
• The example and notebook structure were validated as described above.