Despite their theoretical limitations, ARIMA models are widely used in real-life forecasting tasks. Parzen has proposed an extension of ARIMA models: ARARMA models. ARARMA models consist of an AR model followed by an ARMA model. Following Parzen approach,-NARMA neural network are MLP, the units of which are simple non-linear ARMA-based models (-NARMA units). They are a non-linear extension of A...

This paper addresses the problem of deriving asymptotic distribution empirical function Fˆn residuals in a general class time series models, including conditional mean and heteroscedaticity, whose independent identically distributed errors have unknown F. We show that, for large models (including standard ARMA-GARCH with symmetric innovations), n{Fˆ n(·)?F(·)} is impacted by estimation but does...

In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M0 and M1, introduced by Piccolo in 1990. In particular, we show that this set of linear restrictions is equivalent to a null distance d(M0,M1) between two given ARMA mo...

The adequate modeling of correlated input processes is an important step in building simulation models. Modeling independent identically distributed data is well established in simulation whereas the integration of correlation is still a challenge. In this paper, ARTA processes which have been used several times for describing correlated input processes in simulation are extended by using ARMA ...

Time Series Forecasting (TSF) allows the modeling of complex systems as “black-boxes”, being a focus of attention in several research arenas such as Operational Research, Statistics or Computer Science. Alternative TSF approaches emerged from the Artificial Intelligence arena, where optimization algorithms inspired on natural selection processes, such as Evolutionary Algorithms (EAs), are popul...

Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential regimes. Although statistical issues have been the subject of many recent papers, there is few systematic study of the probabilistic aspects of this new class of n...

This paper reports the feasibility of the ARMA model to describe a bursty video source transmitting over a AAL5 ATM link (VBR traffic). The traffic represents the activity of the action movie "Lethal Weapon 3" transmitted over the ATM network using the Fore System AVA-200 ATM video codec with a peak rate of 100 Mbps and a frame rate of 25. The model parameters were estimated for a single video ...

How strongly natural populations are regulated has a long history of debate in ecology. Here, we discuss concepts of population regulation appropriate for stochastic population dynamics. We then analyse two large collections of data sets with autoregressive-moving average (ARMA) models, using model selection techniques to find best-fitting models. We estimated two metrics of population regulati...

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...