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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Modified Maximum Likelihood Estimation in Autoregressive Processes with Generalized Exponential Innovations

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DOI: 10.4236/ojs.2014.48058 3,319 Downloads 4,088 Views

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Bernardo Lagos-Álvarez¹, Guillermo Ferreira¹, Emilio Porcu²

Affiliation(s)

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

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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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