A Bayesian approach is developed to generate constrained and unconstrained forecasts in autoregressive-moving average time series models. Both are calculated by formulating the ARMA(p,q) model in such a way that it is possible to numerically compute the predictive distribution for any number of forecasts as in de Alba (1993). We obtain the posterior distribution of the parameters via Gibbs samp...

In this paper, our proposal is to combine univariate ARMA models to produce a variant of the VARMA model that is much more easily implementable and does not involve certain complications. The original model is reduced to a series of univariate problems and a copula – like term (a mixture-of-normals densities) is introduced to handle dependence. Since the univariate problems are easy to handle b...

We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To remedy this problem, we replace the deterministic relationships with Gaussian distributions having a small variance, yielding the stochastic ARMA (σARMA) model....

The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by Xs,t = i≥0 j≥0 a i,j ξ s−i,t−j , (s, t) ∈ Z 2 , where the ξ i,j are independent and identically distributed, zero mean innovations. By judicious choice of σ−fields and element enumeration, one dimensional martingale arguments are employed to establish t...

We extend the standard covariance function used in the Gaussian Process prior nonparametric modelling approach to include correlated (ARMA) noise models. The improvement in performance is illustrated on some simulation examples of data generated by nonlinear static functions corrupted with additive ARMA noise. 1 Gaussian Process priors In recent years many flexible parametric and semi-parametri...

Modeling the dependency between stock market returns is a difficult task when returns follow a complicated dynamics. It is not easy to specify the multivariate distribution relating two or more return series. In this paper, a methodology based on fitting ARIMA, GARCH and ARMA-GARCH models and copula functions is applied. In such methodology, the dependency parameter can easily be rendered condi...

Given observations on a stationary economie vector time series process we show that the best % periods ahead forecast (best in the sense of having minimal forecast error variance) of one of the variables can be consistently estimated by nonparametric regression on an ARMA memory index. Our approach is based on a combination of the ARMA memory index modeling approach of Bierens (1986a) with a mo...

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...

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...