# Using simulation to compare the two estimation methods (ML) and (FGNLS) of the RCPAR periodic autoregressive model with random coefficient (1)

## DOI:

https://doi.org/10.31272/jae.i139.1089## Keywords:

RCPAR (1) model, , PAR (1) model, FGNLS estimator, ML estimator## Abstract

The first-order random coefficient periodic autoregressive model RCPAR(1) was introduced by researchers (Frances and Paap, 2011), due to its importance in the field of seasonal time series applications, and its reduction of the number of parameters in the unrestricted periodic autoregressive model PAR(1). , as the increasing number of parameters results in a problem in the estimation stage. Thus, this stage was studied using the method of greatest possibility (ML) and the method of possible nonlinear least squares (FGNLS) and comparing them through the application of three simulation experiments using the Monte-Carlo method. It was concluded that there is a clear bias for small samples in the estimators of (ML), and then the preference of the (FGNLS) method in estimating the parameters of the RCPAR (1) model over the (ML) method for all samples used.

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