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Poster Communications<br />
SP1<br />
Wednesday, September 4th<br />
19:45<br />
A new autorregressive moving average model<br />
based on the unit Rayleigh distribution for rates<br />
and proportions: a simulation study<br />
Renata Rojas Guerra<br />
UFSM<br />
Fernando A. Peña-Ramírez<br />
The unit Rayleigh (UR) is a one-parameter model that is suitable to accommodate asymmetric<br />
unimodal data. It was pioneered Mazucheli et. al. (2018) as a special case of the unit Weibull<br />
distribution. From the results of Guerra (2019), we can cite two main advantages of this model.<br />
The first one is that it presents the maximum likelihood estimator in closed-form. Secondly, it<br />
has a simple expression for the median. In this work, we consider a median re-parametrization<br />
for the UR distribution and propose an autoregressive moving average structure based on this.<br />
We aim to provide a simple alternative for modeling double bounded variables under the presence<br />
of serial correlation in the conditional median of the UR distribution. Once the parent model is<br />
a one-parameter distribution, the introduced model is more parsimonious than the most popular<br />
autoregressive moving average time series. We discuss a conditional maximum likelihood approach<br />
to estimate the model parameters and present a Monte Carlo simulation study to assess its finite<br />
sample performance.<br />
Keywords: ARMA models; Bounded data; Unit Rayleigh distribution<br />
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