Extract Residuals of KFS output
# S3 method for KFS
residuals(object, type = c("recursive", "pearson", "response", "state"), ...)KFS object
Character string defining the type of residuals.
Ignored.
For object of class KFS, several types of residuals can be computed:
"recursive": One-step-ahead prediction residuals
\(v_{t,i}=y_{t,i}-Z_{t,i}a_{t,i}\). For non-Gaussian case recursive
residuals are computed as \(y_{t}-f(Z_{t}a_{t})\), i.e.
non-sequentially. Computing recursive residuals for large non-Gaussian
models can be time consuming as filtering is needed.
"pearson": $$(y_{t,i}-\theta_{t,i})/\sqrt{V(\mu_{t,i})},
\quad i=1,\ldots,p,t=1,\ldots,n,$$ where \(V(\mu_{t,i})\) is the
variance function of the series \(i\)
"response": Data minus fitted values, \(y-E(y)\).
"state": Residuals based on the smoothed disturbance terms
\(\eta\) are defined as $$\hat \eta_t, \quad t=1,\ldots,n.$$
Only defined for fully Gaussian models.