smooth.MSARIMA.sigma

property MSARIMA.sigma: float

sigma(adam_obj)).

Mirrors R’s sigma.adam (R/adam.R:4625-4658): df-adjusted sum of squared residuals (with a distribution-specific transformation for log-domain and multiplicative distributions). For likelihood loss the scale parameter is subtracted from nparam to match R’s convention.

For the common case (dnorm / dlaplace / ds / dgnorm / dt / dlogis / dalaplace) this is sqrt(sum(residuals²) / (nobs − nparam + 1)) when loss is likelihood, or sqrt(sum(residuals²) / (nobs − nparam)) otherwise.

Use scale if you want the model’s internal optimisation scale (R: adam_obj$scale) — they coincide only for dnorm but differ for non-normal distributions where the optimisation scale parameterises the density and the empirical residual std is a separate scalar.

Type:

Empirical residual standard deviation (R