Burg estimators are classically used for the estimation of the autocovariance of a stationary autoregressive process. We propose to consider scale mixtures of stationary autoregressive processes, a non-Gaussian extension of the latter. The traces of such processes are Spherically Invariant Random Vectors (SIRV) with a constraint on the scatter matrix due to the autoregressive model. We propose ...

A class of nonstationary time series such as locally stationary time series can be approximately modeled by piecewise stationary autoregressive (PSAR) processes. But the number and locations of the piecewise autoregressive segments, as well as the number of nonzero coefficients in each autoregressive process, are unknown. In this talk, by connecting the multiple structural break detection with ...

In this paper, an original Markov-switching autoregressive model is proposed to describe the space-time evolution of wind fields. At first, a non-observable process is introduced in order to model the motion of the meteorological structures. Then, conditionally to this process, the evolution of the wind fields is described by using autoregressive models whith time varying coefficients. The prop...

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...

S1. PROOF OF INCONSISTENCY OF A QMLE IN THIS SUPPLEMENTAL section we prove that, for an autoregressive process, the gradient of the quasi-log-likelihood does not equal zero when evaluated at the population parameter values. Recall the mixture model for an autoregressive process (1 −π) ·N(θ1 + αXt−1 1)+πN(θ2 + αXt−1 1) (S1) on which the quasi-likelihood is based. For θ1 = μ and θ2 = μ+ γ, we have

We present a methodology for generating probabilistic predictions for the Disturbance Storm Time (Dst) geomagnetic activity index. We focus on the One Step Ahead prediction task and use the OMNI hourly resolution data to build our models. Our proposed methodology is based on the technique of Gaussian Process Regression. Within this framework we develop two models; Gaussian Process Autoregressiv...

In this paper we present an autoregressive model with neural networks modeling and standard error backpropagation algorithm training optimization in order to predict the gross domestic product (GDP) growth rate of four countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1))...