arima_pi: Prediction Intervals for ARIMA Processes with Exogenous...

In helske/tsPI: Improved Prediction Intervals for ARIMA Processes and Structural Time Series

Prediction Intervals for ARIMA Processes with Exogenous Variables Using Importance Sampling

Description

Function arima_pi computes prediction intervals for ARIMA processes with exogenous variables using importance sampling. For regression coefficients, diffuse (uninformative) prior is used, whereas multiple options for prior distributions for ARMA coefficients are supported.

Usage

arima_pi(
  x,
  order,
  xreg = NULL,
  n_ahead = 1,
  level = 0.95,
  median = TRUE,
  se_limits = TRUE,
  prior = "uniform",
  custom_prior,
  custom_prior_args = NULL,
  nsim = 1000,
  invertibility = FALSE,
  last_only = FALSE,
  return_weights = FALSE,
  ...
)

Arguments

x	vector containing the time series
order	vector of length 3 with values p,d,q corresponding to the number of AR parameters, degree of differencing and number of MA parameters.
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 AR and MA parameters. Defaults to uniform prior. Several Jeffreys' priors are also available (see jeffreys for details). If "custom", a user-defined custom prior is used (see next arguments). All priors assume that the ARMA parameters lie in stationarity/invertibility region.
custom_prior	function for computing custom prior. First argument must be a vector containing the AR and MA parameters (in that order).
custom_prior_args	list containing additional arguments to custom_prior.
nsim	number of simulations used in importance sampling. Default is 1000.
invertibility	Logical, should the priors include invertibility constraint? Default is FALSE.
last_only	compute the prediction intervals only for the last prediction step.
return_weights	Return (scaled) weights used in importance sampling.
...	additional arguments for arima.

Value

a list containing the prediction intervals. @references

1. Helske, J. and Nyblom, J. (2015). Improved frequentist prediction intervals for autoregressive models by simulation. In Siem Jan Koopman and Neil Shephard, editors, Unobserved Components and Time Series Econometrics. Oxford University Press. https://urn.fi/URN:NBN:fi:jyu-201603141839

2. Helske, J. and Nyblom, J. (2014). Improved frequentist prediction intervals for ARMA models by simulation. In Johan Knif and Bernd Pape, editors, Contributions to Mathematics, Statistics, Econometrics, and Finance: essays in honour of professor Seppo Pynnönen, number 296 in Acta Wasaensia, pages 71–86. University of Vaasa. https://urn.fi/URN:NBN:fi:jyu-201603141836

See Also

tsPI, struct_pi

Examples

set.seed(123)
x <- arima.sim(n = 30, model = list(ar = 0.9))

pred_arima <- predict(arima(x, order = c(1,0,0)), n.ahead = 10, se.fit = TRUE)
pred_arima <- cbind(pred = pred_arima$pred,
  lwr = pred_arima$pred - qnorm(0.975)*pred_arima$se,
  upr = pred_arima$pred + qnorm(0.975)*pred_arima$se)

pred <- arima_pi(x, order = c(1,0,0), n_ahead = 10)

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

helske/tsPI documentation built on Sept. 9, 2023, 8:15 a.m.