struct_pi {tsPI}

Prediction Intervals for Structural Time Series with Exogenous Variables Using Importance Sampling

Description

Function struct_pi computes prediction intervals for structural time series with exogenous variables using importance sampling.

Usage

struct_pi(
  x,
  type = c("level", "trend", "BSM"),
  xreg = NULL,
  n_ahead = 1,
  level = 0.95,
  median = TRUE,
  se_limits = TRUE,
  prior = "uniform",
  custom_prior,
  custom_prior_args = NULL,
  nsim = 1000,
  inits = NULL,
  last_only = FALSE,
  return_weights = FALSE
)

Arguments

x

vector containing the time series

type

type of model. Possible options are "level", "trend" and "BSM", corresponding to local level, local linear trend, and local linear trend model with seasonal component.

xreg

matrix or data frame containing the exogenous variables (not including the intercept which is always included for non-differenced series)

n_ahead

length of the forecast horizon.

level

desired frequentist coverage probability of the prediction intervals.

median

compute the median of the prediction interval.

se_limits

compute the standard errors of the prediction interval limits.

prior

prior to be used in importance sampling for log-sd parameters. Defaults to uniform prior on logarithm of standard deviations (with constraints that all variances are smaller than 1e7). If "custom", a user-defined custom prior is used (see next arguments).

custom_prior

function for computing custom prior. First argument must be a vector containing the log-variance parameters (observation error, level, slope, and seasonal).

custom_prior_args

list containing additional arguments to custom_prior.

nsim

number of simulations used in importance sampling. Default is 1000.

inits

initial values for log-sds

last_only

compute the prediction intervals only for the last prediction step.

return_weights

Return (scaled) weights used in importance sampling.

Value

a list containing the prediction intervals.

See Also

tsPI, arima_pi @references

1. Helske, J. (2015). Prediction and interpolation of time series by state space models. University of Jyväskylä. PhD thesis, Report 152. https://urn.fi/URN:NBN:fi:jyu-201603111829

Examples

pred_StructTS <- predict(StructTS(Nile, type ="level"), n.ahead = 10, se.fit = TRUE)
pred_StructTS <- cbind(pred = pred_StructTS$pred,
  lwr = pred_StructTS$pred - qnorm(0.975)*pred_StructTS$se,
 upr = pred_StructTS$pred + qnorm(0.975)*pred_StructTS$se)

set.seed(123)
pred <- struct_pi(Nile, type = "level", n_ahead = 10)

ts.plot(ts.union(Nile,pred_StructTS, pred[,1:3]), col = c(1,2,2,2,3,3,3),
  lty = c(1,1,2,2,1,2,2))