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Three serial-correlation diagnostics, at statsmodels 0.15.0 parity: the sample autocorrelation function, its partial counterpart, and the Ljung-Box portmanteau test — a correlogram, and the test that says whether it matters.

diagnostic	what it asks	entry point
autocorrelation	how strongly does the series echo itself at each lag?	SerialCorrelation.Autocorrelation
partial autocorrelation	the same, with the shorter lags' influence on longer ones removed	SerialCorrelation.PartialAutocorrelation
Ljung-Box	is any of it more than noise?	SerialCorrelation.LjungBox

All three are static methods on SerialCorrelation, each taking a ReadOnlySpan<double> series and a required lag count. The reference defaults the lag count, and to two different rules depending on which function is asked — min(10·log10(n), n - 1) for acf, min(10·log10(n), n/2 - 1) for pacf — so this asks rather than silently picking one; pass either rule deliberately to reproduce a reference plot.

result	carries	returned by
AutocorrelationResult	the sequence and its band, indexed from lag 0	SerialCorrelation.Autocorrelation, SerialCorrelation.PartialAutocorrelation
LjungBoxResult	five lists cumulated lag by lag, indexed from lag 1	SerialCorrelation.LjungBox

Two option records choose what a call is told; neither has a public constructor of its own to speak of beyond the defaults, and both are validated where a property is set rather than where it is later read.

option	chooses
AutocorrelationOptions	the estimator, the band shape, and its confidence level
LjungBoxOptions	the model's parameter count, and whether Box-Pierce is reported beside Ljung-Box

The Python equivalence table maps each statsmodels call to its counterpart here.