Compute Out-of-Sample Inference for Fitted State Space Model

Applies the fitted model parameters to a user-supplied out-of-sample dataset to compute predicted and filtered states and observations. Robust and classical inference procedures are supported depending on the class of the input model.

Usage

oos_filter(
  y_oos,
  model,
  build,
  outlier_locs = rep(0, nrow(y_oos)),
  threshold = sqrt(qchisq(0.99, ncol(y_oos))),
  multiplier = 2
)

Arguments

y_oos

A numeric matrix containing out-of-sample observations. Each row corresponds to a time point.

model

A fitted model object of class roams_SSM, classical_SSM, oracle_SSM, huber_robust_SSM, or trimmed_robust_SSM.

build

A function that maps a numeric parameter vector to a corresponding dlm model object. The specify_SSM function can be used to create this build function.

outlier_locs

A logical or binary vector of the same length as nrow(y), indicating time points to be treated as missing (i.e., time points that are known to be outliers). Used only with oracle_SSM models.

threshold

Mahalanobis distance threshold for detecting out-of-sample outliers in roams_SSM models. Set to Inf to recover the usual Kalman filter. Default is sqrt(qchisq(0.99, ncol(y))).

multiplier

Multiplier for how quickly the filter grows its filtered state variance (uncertainty) after detecting an outlier in roams_SSM models. It is the tuneable parameter \(b\) of the `fast-updating threshold' filter. Only works if threshold is not Inf. Default is 2.

Value

A named list containing out-of-sample inference results:

filtered_states

Filtered state estimates using out-of-sample data.

predicted_states

One-step-ahead state predictions.

filtered_observations

Expected observations given past out-of-sample data.

predicted_observations

One-step-ahead forecasts of observations.

filtered_states_var

List of filtered state variance matrices.

predicted_states_var

List of one-step-ahead state prediction variances.

predicted_observations_var

List of one-step-ahead observation forecast variances.

mahalanobis_residuals

Vector of Mahalanobis distances of residuals from predicted observations.

outliers_flagged

Vector of 1's and 0's indicating whether timepoints are flagged as outlying or not based on the threshold supplied (only available if model is of class roams_SSM).

Details

The function reuses the model's fitted parameters to generate inference on new data y_oos. Robust variants use appropriate robust filters, while the classical and oracle models use standard Kalman filtering. For oracle_SSM models, observations flagged in outlier_locs are treated as missing during filtering.

See also

attach_insample_info, specify_SSM