A distance between pairs of sets of autoregressive moving average (ARMA) processes is proposed. Its main properties are discussed. The paper also shows how the proposed distance finds application in time series analysis. In particular it can be used to evaluate the distance between portfolios of ARMA models or the distance between vector autoregressive (VAR) models.

Recently, there are much works on developing models suitable for analyzing the volatility of a discrete-time process. Within the framework of Auto-Regressive Moving-Average (ARMA) processes, we derive a necessary and sufficient condition for the kernel to be non-negative. This condition is in terms of the generating function of the ARMA kernel which has a simple form. We discuss some useful con...

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where ...

We de2ne a notion of subspace angles between two linear, autoregressive moving average, single-input–single-output models by considering the principal angles between subspaces that are derived from these models. We show how a recently de2ned metric for these models, which is based on their cepstra, relates to the subspace angles between the models. c © 2002 Elsevier Science B.V. All rights rese...

A new approach for using Lévy processes to compute value at risk (VaR) using high-frequency data is presented in this paper. The approach is a parametric model using an ARMA(1,1)-GARCH(1,1) model where the tail events are modeled using the fractional Lévy stable noise and Lévy stable distribution. Using high-frequency data for the German DAX Index, the VaR estimates from this approach are compa...

The combination forecasting model IOWGA-EMD-ARMA-WNN is proposed in this paper. The randomness, periodicity and tendency of the original data are showed by EMD decomposition in EMD-ARMA model. WNN combines the advantages of wavelet analysis and BP neural network and improves the learning efficiency and forecasting accuracy. The weight of combination model is decided by forecasting precision of ...