Start by clarifying that population standard deviation uses n and treats the window as the entire population, while sample standard deviation uses n-1 to correct bias when the window is a sample from a larger process. Then explain the practical implications for rolling estimates, edge cases, and implementation choices, emphasizing configurability and documentation.
Pro tip: In trading contexts, the choice between n and n-1 is often less important than consistency and clear documentation; however, for small windows (e.g., <30), the difference can materially affect volatility estimates, so default to sample (n-1) unless the window is explicitly the full population.
Explain that population standard deviation divides by n (the number of observations) and assumes the window contains all possible values, while sample standard deviation divides by n-1 (Bessel's correction) to produce an unbiased estimator when the window is a sample from a larger population.
Describe how using n vs n-1 affects the magnitude of rolling volatility, especially for small windows; n-1 yields slightly larger estimates, which can matter for risk calculations and signal generation.
State that for a window of size 1, population standard deviation is 0 (since the single value is the mean), while sample standard deviation is undefined (division by zero); decide whether to return NaN, 0, or raise an error based on context.
Recommend defaulting to sample standard deviation (n-1) for general use, but allow a parameter (e.g., ddof) to switch to population; ensure the implementation supports both and that the choice is explicit.
Document the parameter, its default, and the implications (e.g., bias, edge cases) in docstrings and user-facing documentation, including examples for small windows.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.