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...

The merits of the modelling philosophy of Box & Jenkins (1970) are illustrated with a summary of our recent work on seasonal river flow forecasting. Specifically, this work demonstrates that the principle of parsi-mony, which has been questioned by several authors recently, is helpful in selecting the best model for forecasting seasonal river flow. Our work also demonstrates the importance of m...

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...

When it comes to measuring inflation persistence, a common practice in empirical research is to estimate univariate autoregressive moving average (ARMA) time series models and measure persistence as the sum of the estimated AR coefficients. We examine four potential sources of lag dynamics in inflation: the evolution of policymakers‟ willingness to stabilize output, shifts in the mean inflation...

In this paper the boundaries of several families of (time-invariant) ARMA models and corresponding linear state space models are described. The topology of pointwise convergence of the Markov parameters is used.

Ten candidate models of the Auto-Regressive Moving Average (ARMA) family are investigated for representing and forecasting monthly and ten-day streamflow in three Indian rivers. The best models for forecasting and representation of data are selected by using the criteria of Minimum Mean Square Error (MMSE) and Maximum Likelihood (ML) respectively. The selected models are validated for significa...