Modified Maximum Likelihood Estimation in Autoregressive Processes with Generalized Exponential Innovations

Bernardo Lagos-Álvarez; Guillermo Ferreira; Emilio Porcu

doi:10.4236/ojs.2014.48058

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Open Journal of Statistics > Vol.4 No.8, September 2014

Modified Maximum Likelihood Estimation in Autoregressive Processes with Generalized Exponential Innovations ()

Bernardo Lagos-Álvarez¹, Guillermo Ferreira¹, Emilio Porcu²

¹Department of Statistics, Universidad de Concepción, Concepción, Chile.
²Department of Mathematics, University Federico Santa María, Valparaíso, Chile.

DOI: 10.4236/ojs.2014.48058 PDF HTML 3,691 Downloads 4,476 Views

Abstract

We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.

Keywords

Autoregressive Time Series Model, Maximum Likelihood, Modified Maximum Likelihood, Least Squares, Generalized Exponential

Share and Cite:

Lagos-Álvarez, B. , Ferreira, G. and Porcu, E. (2014) Modified Maximum Likelihood Estimation in Autoregressive Processes with Generalized Exponential Innovations. Open Journal of Statistics, 4, 620-629. doi: 10.4236/ojs.2014.48058.

Conflicts of Interest

The authors declare no conflicts of interest.

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