An optimal prediction in general ARMA models

Kernel smoothed prediction intervals for ARMA models

Optimal Estimation of Multivariate ARMA Models

Autoregressive moving average (ARMA) models are a fundamental tool in time series analysis that offer intuitive modeling capability and efficient predictors. Unfortunately, the lack of globally optimal parameter estimation strategies for these models remains a problem: application studies often adopt the simpler autoregressive model that can be easily estimated by maximizing (a posteriori) like...

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...

Optimal Instrumental Variables Estimation for ARMA Models

In this paper a new class of Instrumental Variables estimators for linear processes and in particular ARMA models is developed. Previously, IV estimators based on lagged observations as instruments have been used to account for unmodelled MA(q) errors in the estimation of the AR parameters. Here it is shown that these IV methods can be used to improve efficiency of linear time series estimators...

Lecture 2 : ARMA Models ∗ 1 ARMA Process

As we have remarked, dependence is very common in time series observations. To model this time series dependence, we start with univariate ARMA models. To motivate the model, basically we can track two lines of thinking. First, for a series xt, we can model that the level of its current observations depends on the level of its lagged observations. For example, if we observe a high GDP realizati...