We are interested in modeling a zero mean heteroscedastic time series process with autoregressive error process of finite known order p. The model can be used for testing a martingale difference sequence hypothesis that is often adopted uncritically in financial time series against a fairly general alternative. When the argument is deterministic, we provide an innovative nonparametric estimator...

Let {Y :n ~ o} be a Harris-recurrent Markov chain on a general state n space. It is shown that {Y J is strong mixing, provided there exists a n stationary probability distribution ~(.) for {Y}. We use this result to n establish that certain stationary autoregressive moving average processes are strong mixing. Necessary and sufficient conditions for a first order autoregressive process to be uni...

We study the properties of an MA1-representation of an autoregressive a p p r o x-imation for a stationary, real-valued process. In doing so we g i v e an extension of Wiener's Theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain insight i n to the structure of MA1-representations of tted autoregressive models where the order increas...

Time series analysis of fertility can improve demographic forecasts. The optimal forecast and its variance for births to an age-structured population subject to serially correlated random fertility are developed. The general case in which the fertility process had arbitrary autoregressive structure is dealt with and then the 4 special cases of white noise, 1st-order autoregressive, 2nd-order ...

In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh–...

This paper addresses estimation of general linear processes under the relevant loss function using autoregressive approximations. The estimators of the autoregressive parameters are shown to be consistent in the sense that the L1 norm of the distance to the respective true values converges in probability to zero. The assumptions on the order of the approximation and the moment requirements for ...

In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. These methods have advantages compared with common Fourier techniques concerning their inherent stationarity and physical background. However, if autoregressive models are used, it has to be taken into account that real data always contain ...

We consider the sets of moving-average and autoregressive processes and study their closures under the Mallows metric and the total variation convergence on nite dimensional distributions. These closures are unexpectedly large, containing nonergodic processes which are Poisson sums of i.i.d. copies from a stationary process. The presence of these non-ergodic Poisson sum processes has immediate ...

A multichannel extension of the AR matrix prewhitened power spectral density estimator, which was originally developed for a single channel, is proposed. In order to make the extension, the Cholesky decomposition of the inverse autocorrelation matrix for a multichannel autoregressive process is discussed and the autoregressive model order selection for a multichannel process based on the expone...