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Fits a VAR of the given lag order and reports what a summary table holds.

public static VarSummary Fit(ReadOnlySpan<double> series, int variableCount, int lagOrder, VarOptions options = null)

Parameters — series is the observations, row-major in time: variableCount values each, oldest first. variableCount is how many variables an observation carries, at least two. lagOrder is how many lags enter each equation, at least one. options chooses whether each equation carries a constant; null fits one, the reference's trend="c".

Returns — VarSummary: the coefficients per equation with their standard errors, t statistics and p-values, the two residual covariances, the log-likelihood and the four criteria.

Exceptions — ArgumentOutOfRangeException when variableCount is below two — one variable is an autoregression rather than a vector one — or when lagOrder is below one. ArgumentException when series is empty or not a whole number of observations, when it holds a value that is not finite, or when the lags leave no residual degree of freedom: n − lagOrder usable rows must exceed the (1 or 0) + variableCount·lagOrder parameters each equation fits. Also when the lagged design is collinear — a variable proportional to another, for instance — with a smallest singular value at or below σmax·max(n, p)·ε, numpy.linalg.matrix_rank's tolerance and the one Lodestar.Stats.Regression's fits refuse at.

Example — the second equation of a two-variable system, and what the whole model scores.

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, variableCount: 2, lagOrder: 1);

double crossLag = Math.Round(fit.Coefficients[1][1], 6);     // => 0.624949
double itsError = Math.Round(fit.StandardErrors[1][1], 6);   // => 0.176406
double itsP = Math.Round(fit.PValues[1][1], 6);              // => 0.000396
double logLikelihood = Math.Round(fit.LogLikelihood, 6);     // => -10.899549

The second series depends on the first's previous value with a coefficient of 0.625 and a p-value of 0.0004, on the 14 usable observations these 15 rows leave at lag 1.

Remarks — the parameters run in the reference's own order: the constant when one was fitted, then lag 1's coefficient for every variable, then lag 2's. Equation j explains variable j.

The tests read the normal, not Student's t, which is what statsmodels does for this model, and no intervals are reported because the reference publishes none — its VARResults has no conf_int.

Lag-order selection, impulse responses, forecast-error variance decomposition and Granger causality are not here; each waits for a caller, as decision 0003 asks.

Applies to — net10.0, netstandard2.0.

See also — VarSummary, VarOptions.