Prediction Intervals for ARIMA Models

ARIMA-GARCH and unobserved component models with GARCH disturbances: Are their prediction intervals different?∗

We analyze the effects on prediction intervals of fitting ARIMA models to series with stochastic trends, when the underlying components are heteroscedastic. We show that ARIMA prediction intervals may be inadequate when only the transitory component is heteroscedastic. In this case, prediction intervals based on the unobserved component models tend to the homoscedastic intervals as the predicti...

Prediction Intervals for Multilevel Models

There are many methods for constructing prediction intervals for differences in observations. This document will explain several of these methods in the context of different models using data from a kiwi yield experiment as an example. 1. KIWI DATA In an experiment (discussed in more detail in class), kiwi yields were measured in a designed experiment. There were three blocks (north, east, and ...

Prediction intervals for regression models

This paper presents simple large sample prediction intervals for a future response Yf given a vector xf of predictors when the regression model has the form Yi = m(xi) + ei where m is a function of xi and the errors ei are iid. Intervals with correct asymptotic coverage and shortest asymptotic length can be made by applying the shorth estimator to the residuals. Since residuals underestimate th...

Kernel smoothed prediction intervals for ARMA models

Abstract The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this paper we apply nonparametric quantile regression to the empirical forecast errors using lead t...

Kernel smoothed prediction intervals for ARMA models