tsPI (version 1.0.4)

arima_pi: 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,
  ...
)

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

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.

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))