Calculate one-step-ahead (OSA) residuals for stochastic volatility model.

The OSA residual of observation y_t is qnorm(F_t(y_t)), where F_t is the predictive distribution function of y_t given y_1, ..., y_{t-1} at the estimated parameters. If the model is correct, the residuals are independent and standard gaussian.

Usage

# S3 method for class 'stochvolTMB'
residuals(
  object,
  conditional = NULL,
  method = c("grid", "tmb"),
  grid_size = 500,
  ...
)

Arguments

object: A stochvolTMB object.
conditional: Index vector of observations that are not predicted. Residuals are returned for the other observations. If NULL, the "grid" method returns residuals for all observations, and the "tmb" method uses 1:(object$nobs - 100). Use integer(0) to get all residuals with "tmb".
method: "grid" or "tmb". See details.
grid_size: Number of grid points for h_t in the "grid" method.
...: Currently not used.

Value

Vector of one-step-ahead residuals. If the model is correctly specified, these should be standard normal.

Details

Two methods are available:

"grid" (default): an exact filter on a grid for the log-volatility h_t. Because h_t is one-dimensional, the predictive distribution can be calculated by summation over the grid, without the Laplace approximation. It calculates the residuals for all observations in a few seconds.
"tmb": oneStepPredict with method = "oneStepGeneric". It uses the Laplace approximation and takes about one to three seconds per observation, so by default only the last 100 observations are used. It is not available for the "skew_t_leverage" model, where y_t also enters the model for h_{t+1}.

References

Thygesen, U. H., Albertsen, C. M., Berg, C. W., Kristensen, K. and Nielsen, A. (2017). Validation of ecological state space models using the Laplace approximation. Environmental and Ecological Statistics, 24(2), 317-339. doi:10.1007/s10651-017-0372-4