Coventry University, Coventry, CV1 5FB, U.K In this article, we build Box-Jenkins ARMA model and ARMA-GARCH model to forecast the returns of shanghai stock exchange composite index in financial engineering. Out-of-sample forecasting performances are evaluated to compare the forecastability of the two models. Traditional engineering type of models aim to minimize statistical errors, however, the...

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...

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR r...

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...

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...

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...

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....