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.

The Classical statistical inference for integer valued time-series has primarily been restricted to the integer valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer valued time-series where statistical inference is greatly assisted by data augmentation. Thus in ...

We present a bayesian method for the blind estimation of parameters in nonlinear/nongaussian models. The studied models are called H-ARMA processes. They are generated by a memoryless polynomial transformation of an ARMA process. The nonlinearities are choosen as Her-mite polynomials. After recalling the structure of those models and their main properties that have been reported in previous pub...

Abstract: Easily computable recursive algorithms are proposed for estimating coefficients of A(z), C(z), and the covariance matrix Rw of wk for the multivariate ARMA process A(z)yk = C(z)wk on the basis of the noise-corrupted observations ηk ∆ = yk + ǫk. It is shown that the estimates converge to the true ones under reasonable conditions. An illustrative example is provided, and the simulation ...

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...

Since the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and...

The study has two aims. The first aim is to propose a family of nonlinear GARCH models that incorporate fractional integration and asymmetric power properties to MS-GARCH processes. The second purpose of the study is to augment the MS-GARCH type models with artificial neural networks to benefit from the universal approximation properties to achieve improved forecasting accuracy. Therefore, the ...