MARSS (version 3.4)

residuals.marssMLE: MARSS standardized residuals

Description

Calculates the standardized (or auxilliary) residuals sensu Harvey, Koopman and Penzer (1998). This is a utility function in the MARSS-package.

Usage

## S3 method for class 'marssMLE':
residuals(object,...)

Arguments

object

An object of class marssMLE. This object must have $par, $model and $kf elements containing MLE parameter estimates from e.g.

...

Not used.

Value

• A list with the following components
• vthat
  The smoothed model residuals y(t)-E(y(t)|y(1:T),Theta), where Theta is the set of model parameters (Z, A, R, etc). Sometimes called the smoothations. This is different than the Kalman filter innovations which are y(t)-E(y(t)|y(1:t-1),Theta).
• wthat
  The smoothed stated residuals E(x(t)|y(1:T))-E(x(t)|E(x(t-1)|y(1:T))).
• et
  The model residuals as a (n+m) x TT matrix with vthat on top and wthat below. et is hat(eta_t) on page 112 of Harvey, Koopman and Penzer (1998).
• var.et
  The variance of the model residuals as a (n+m) x (n+m) x TT matrix. This is var(hat(eta_t)).
• std.et
  The standardized model residuals as a (n+m) x TT matrix. This is et divided by the square root of var.et --- although the code is using the matrix equivalent of that equation.

Details

Uses the algorithm on page 112 of Harvey, Koopman and Penzer (1998) to compute the standardized model residuals.

References

Harvey, A., S. J. Koopman, and J. Penzer. 1998. Messy time series: a unified approach. Advances in Econometrics 13: 103-144 (see page 112). Koopman, S. J., N. Shephard, and J. A. Doornik. 1999. Statistical algorithms for models in state space using SsfPack 2.2. Econometrics Journal 2: 113-166. (see pages 147-148).

See Also

MARSSkem marssMLE

Examples

dat = t(harborSeal)
  dat = dat[c(2,11),]
  MLEobj = MARSS(dat)
  
  #not standardized model residuals
  residuals(MLEobj)$model.residuals

  #standardized (by variance) model & state residuals
  residuals(MLEobj)$std.residuals