Note that, as predicted, all the means of the fitted models are all essentially 0, and their variances decrease as k increases.

In this case a parametric model is fitted to the data, often by maximum likelihood, and samples of random numbers are drawn from this fitted model.

A fitted model having been produced, each observation in turn is removed and the model is refitted using the remaining observations.

All other data are then tested against the fitted model and, if a point fits well to the estimated model, also considered as a hypothetical inlier.

The resulting fitted model can be used to summarize the data, to predict unobserved values from the same system, and to understand the mechanisms that may underlie the system.

Different types of plots of the residuals from a fitted model provide information on the adequacy of different aspects of the model.

At a minimum, it can ensure that any extrapolation arising from a fitted model is "realistic" (or in accord with what is known).

Smaller values indicate better fit as the fitted model deviates less from the saturated model.

A small correction must be made to the sum-of-squared residuals in the second-stage fitted model in order that the covariance matrix of is calculated correctly.

Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise.