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.
Highlights
The common model for a stationary time series is the stationary and invertible autoregressive model of order ( ) p AR ( p) where the usual assumption is that the innovations { t} are identically and independently distributed (IID) according to a Gaussian distribution with zero mean and variance σ 2 > 0
The main proposal of our paper is based on the use of modified likelihood as introduced by [13] [14] and [15] under the framework of IID observations, in order to estimate the parameters in the context of simple linear regression with stationary and invertible autoregressive errors of order one with innovations represented by Generalized Exponential distribution; for more details on these distributions the reader refers to [16]
We have studied a regression linear model with first-order autoregressive errors belonging to a class of asymmetric distributions; the underlying distribution for the innovations is a Generalized Exponential distribution
Summary
The common model for a stationary time series is the stationary and invertible autoregressive model of order ( ) p AR ( p) where the usual assumption is that the innovations { t} are identically and independently distributed (IID) according to a Gaussian distribution with zero mean and variance σ 2 > 0. The main proposal of our paper is based on the use of modified likelihood as introduced by [13] [14] and [15] under the framework of IID observations, in order to estimate the parameters in the context of simple linear regression with stationary and invertible autoregressive errors of order one with innovations represented by Generalized Exponential distribution; for more details on these distributions the reader refers to [16] This method is notorious for giving asymptotically fully efficient estimators (for example, see [17]-[20]).
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