predict.bsts: Prediction for bayesian structural time series

Description

Generated draws from the posterior predictive distribution of a bsts object.

Usage

# S3 method for bsts
predict(object,
        newdata = NULL,
        horizon = 1,
        burn = SuggestBurn(.1, object),
        na.action = na.exclude,
        olddata = NULL,
        trials.or.exposure = 1,
        quantiles = c(.025, .975),
        ...)

Arguments

object

An object of class bsts created by a call to the function bsts.

newdata

a vector, matrix, or data frame containing the predictor variables to use in making the prediction. This is only required if object contains a regression compoent. If a data frame, it must include variables with the same names as the data used to fit object. The first observation in newdata is assumed to be one time unit after the end of the last observation used in fitting object, and the subsequent observations are sequential time points. If the regression part of object contains only a single predictor then newdata can be a vector. If newdata is passed as a matrix it is the caller's responsibility to ensure that it contains the correct number of columns and that the columns correspond to those in object$coefficients.

horizon

An integer specifying the number of periods into the future you wish to predict. If object contains a regression component then the forecast horizon is nrow(X), and this argument is not used.

burn

An integer describing the number of MCMC iterations in object to be discarded as burn-in. If burn <= 0 then no burn-in period will be discarded.

na.action

A function determining what should be done with missing values in newdata.

olddata

This is an optional component allowing predictions to be made conditional on data other than the data used to fit the model. If omitted, then it is assumed that forecasts are to be made relative to the final observation in the training data. If olddata is supplied then it will be filtered to get the distribution of the next state before a prediction is made, and it is assumed that the first entry in newdata comes immediately after the last entry in olddata.

The value for olddata depends on whether or not object contains a regression component.

If a regression component is present, then olddata is a data.frame including variables with the same names as the data used to fit object, including the response .

If no regression component is present, then olddata is a vector containing historical values of a time series.

trials.or.exposure

For logit or Poisson models, the number of binomial trials (or the exposure time) to assume at each time point in the forecast period. This can either be a scalar (if the number of trials is to be the same for each time period), or it can be a vector with length equal to horizon (if the model contains no regression term) or nrow(newdata) if the model contains a regression term.

quantiles

A numeric vector of length 2 giving the lower and upper quantiles to use for the forecast interval estimate.

…

This is a dummy argument included to match the signature of the generic predict function. It is not used.

Value

Returns an object of class bsts.prediction, which is a list with the following components.

mean

A vector giving the posterior mean of the prediction.

interval

A two (column/row?) matrix giving the upper and lower bounds of the 95 percent credible interval for the prediction.

distribution

A matrix of draws from the posterior predictive distribution. Each row in the matrix is one MCMC draw. Columns represent time.

Details

Samples from the posterior distribution of a Bayesian structural time series model. This function can be used either with or without contemporaneous predictor variables (in a time series regression).

If predictor variables are present, the regression coefficients are fixed (as opposed to time varying, though time varying coefficients might be added as state component). The predictors and response in the formula are contemporaneous, so if you want lags and differences you need to put them in the predictor matrix yourself.

If no predictor variables are used, then the model is an ordinary state space time series model.

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.

Examples

Run this code

  data(AirPassengers)
  y <- log(AirPassengers)
  ss <- AddLocalLinearTrend(list(), y)
  ss <- AddSeasonal(ss, y, nseasons = 12)
  model <- bsts(y, state.specification = ss, niter = 500)
  pred <- predict(model, horizon = 12, burn = 100)
  plot(pred)

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