A First Order Non-Stationary Seasonal Autoregressive Model With a Random Coefficient Parameter

Abstract

This research aims to study a first-order seasonal autoregressive model with a random parameter taking different formulas and following the effect of the season on this parameter, assuming that the random errors of the model follows a standard normal distribution. Samples were selected (30, 60, 150, 240) and season lengths (4, 12) and the experiment was repeated 5000 times. One of the main findings is that the value of MSE decreases when increases in sample size and length of the season. Also, it is possible to estimate the parameter value of the model by traditional methods, even if it is a random coefficient. It is also noticed that the model (6) has the lowest MSE value for all sample sizes and different season lengths.

Keywords: Non-Stationary, Autoregressive Model, Seasonal, Random Coefficient,  Exact Likelihood Method