one.step.prediction.errors {bsts}

Prediction Errors

Description

Computes the one-step-ahead prediction errors for a bsts model.

Usage

bsts.prediction.errors(bsts.object,
                       cutpoints = NULL,
                       burn = SuggestBurn(.1, bsts.object),
                       standardize = FALSE)

Arguments

bsts.object

An object of class bsts.

cutpoints

An increasing sequence of integers between 1 and the number of time points in the trainig data for bsts.object, or NULL. If NULL then the in-sample one-step prediction errors from the bsts object will be extracted and returned. Otherwise the model will be re-fit with a separate MCMC run for each entry in 'cutpoints'. Data up to each cutpoint will be included in the fit, and one-step prediction errors for data after the cutpoint will be computed.

burn

An integer giving the number of MCMC iterations to discard as burn-in. If burn <= 0 then no burn-in sample will be discarded.

standardize

Logical. If TRUE then the prediction errors are divided by the square root of the one-step-ahead forecast variance. If FALSE the raw errors are returned.

Details

Returns the posterior distribution of the one-step-ahead prediction errors from the bsts.object. The errors are computing using the Kalman filter, and are of two types.

Purely in-sample errors are computed as a by-product of the Kalman filter as a result of fitting the model. These are stored in the bsts.object assuming the save.prediction.errors option is TRUE, which is the default (See BstsOptions). The in-sample errors are 'in-sample' in the sense that the parameter values used to run the Kalman filter are drawn from their posterior distribution given complete data. Conditional on the parameters in that MCMC iteration, each 'error' is the difference between the observed y[t] and its expectation given data to t-1.

Purely out-of-sample errors can be computed by specifying the 'cutpoints' argument. If cutpoints are supplied then a separate MCMC is run using just data up to the cutpoint. The Kalman filter is then run on the remaining data, again finding the difference between y[t] and its expectation given data to t-1, but conditional on parameters estimated using data up to the cutpoint.

Value

A matrix of draws of the one-step-ahead prediction errors. Rows of the matrix correspond to MCMC draws. Columns correspond to time.

Author(s)

Steven L. Scott [e-mail]

References

Harvey (1990), "Forecasting, structural time series, and the Kalman filter", Cambridge University Press.

Durbin and Koopman (2001), "Time series analysis by state space methods", Oxford University Press.

See Also

bsts, AddLocalLevel, AddLocalLinearTrend, AddSemilocalLinearTrend, SpikeSlabPrior, SdPrior.

Examples

  data(AirPassengers)
  y <- log(AirPassengers)
  ss <- AddLocalLinearTrend(list(), y)
  ss <- AddSeasonal(ss, y, nseasons = 12)

## Not run: 
  model <- bsts(y, state.specification = ss, niter = 500)

## End(Not run)

  errors <- bsts.prediction.errors(model, burn = 100)
  PlotDynamicDistribution(errors$in.sample)

  ## Compute out of sample prediction errors beyond times 80 and 120.
  errors <- bsts.prediction.errors(model, cutpoints = c(80, 120))
  standardized.errors <- bsts.prediction.errors(
      model, cutpoints = c(80, 120), standardize = TRUE)
  plot(model, "prediction.errors", cutpoints = c(80, 120))
  str(errors)     ## three matrices, with 400 ( = 500 - 100) rows
                  ## and length(y) columns