Bootstrap‎, ‎Modified Maximum Likelihood and Moment Estimators Comparison for Parameters of Autoregressive Model with Non-negative Residuals

Document Type : Original Paper


1 Department of Computer Science and Statistics, K.N. Toosi University of Technology, Tehran, Iran.

2 Department of Statistics, Razi University, Kermanshah, Iran.


Normal residual is one of the usual assumptions in autoregressive model but sometimes
in practice we are faced with non-negative residuals. In this paper, we have
considered the autoregressive time series model where the residuals follow exponential
and Weibull family. The estimation of the parameters in autoregressive with
non-negative residuals are studied based on the modified maximum likelihood,
bootstrap and moments estimators. We examine by simulation, the performance of
the proposed estimation methods and found that the bootstrap estimator is the better
one for autoregressive model with non-negative residuals. As a real data analysis, we
have considered the S&P500 data between 1987-2015 as a data set generated from
a first order autoregressive model with non-negative residuals and based on the
model selection criteria we select the optimal model between the competing models.


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