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 ...

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended ...

In this paper we propose a modification of the Divergence Information Criterion (DIC) for the determination of the order of an autoregressive process and show that it is an asymptotically unbiased estimator of the expected overall discrepancy. Further, we use Monte Carlo methods and various Data Generating Processes for small, medium and large sample sizes in order to explore the capabilities o...

VECTOR AUTOREGRESSIVE PROCESSES WITH COMMON CYCLES MASSIMO FRANCHI & PAOLO PARUOLO JANUARY 7, 2009 Abstract. We give necessary and su cient conditions on the autoregressive polynomial for the existence of (possibly polynomial-) serial correlation common features as well as for other forms of common cycles. We characterize the resulting moving average representations. These conditions allow to d...

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian αstable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are n-consistent ...

The power spectrum estimation for a multichannel autoregressive process using prewhitened and postcoloring technique, 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 multichann...