Serial correlation — Lodestar.Stats.TimeSeries — 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.
Stationarity tests — Lodestar.Stats.TimeSeries — Two tests that answer the question a correlogram raises and cannot settle: may this series be modelled as it stands, or does it need differencing or detrending first?
Seasonality — Lodestar.Stats.TimeSeries — Classical decomposition of a series into a trend, a seasonal pattern and a residual, by moving averages, at statsmodels 0.15.0's seasonal_decompose parity.
Vector autoregression — Lodestar.Stats.TimeSeries — One entry point, VectorAutoregression.Fit, which estimates a VAR(p): several series that move together, each explained by every series' own past, with the table statsmodels' VAR(y).fit(p) prints — the coefficients per equation with their standard errors, t statistics and p-values, the residual covariances, the log-likelihood, and the four information criteria.