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What a vector autoregression reports, at statsmodels parity.

public sealed class VarSummary

Properties:

• The coefficient table. Coefficients, StandardErrors, TStatistics and PValues are indexed by equation first, then by parameter. Equation j explains variable j; its parameters are the constant when one was fitted, then lag 1's coefficient for every variable, then lag 2's.
• The residuals' covariance. ResidualCovariance is S/(T − k), the reference's sigma_u, and ResidualCovarianceMaximumLikelihood is S/T, its sigma_u_mle. Both are row-major and symmetric.
• The whole model. LogLikelihood, then Akaike, Bayesian, HannanQuinn and FinalPredictionError, each read off the maximum-likelihood covariance as the reference reads them.
• The shape of the fit. LagOrder, VariableCount, ObservationsUsed (n − LagOrder), ModelDegreesOfFreedom (parameters per equation), ResidualDegreesOfFreedom and HasIntercept.

Example — the residual covariance and the criteria.

using Lodestar.Stats.TimeSeries;

double[] series = [0.1968, -0.1307, 0.2167, -0.8291, 0.2534, 0.0921, 0.2934, -0.0748, -0.2623, 0.2421,
                   0.4235, -0.3523, -0.2909, 0.4475, -0.2417, -0.9916, -0.3567, -0.3337, -1.0869, -0.5651,
                   -0.5519, -1.0074, -1.2172, -0.1457, 0.2603, -0.7061, -0.7272, 0.3055, 0.3998, -0.6067];

VarSummary fit = VectorAutoregression.Fit(series, 2, 1);

double firstVariance = Math.Round(fit.ResidualCovariance[0], 6);   // => 0.233687
double crossCovariance = Math.Round(fit.ResidualCovariance[1], 6); // => 0.006799
double bayesian = Math.Round(fit.Bayesian, 6);                     // => -2.987651
int residualDegrees = fit.ResidualDegreesOfFreedom;                // => 11

Remarks — no intervals. The reference publishes none for this model, so none are reported here rather than inventing a convention the caller would have to check against it.

Applies to — net10.0, netstandard2.0.

See also — VectorAutoregression.Fit, VarOptions.