The use of spectral analysis in estimating the approximate maximum possibility method using simulation

Abstract

This research aims to choose an appropriate parametric model to represent the data as a model for the studied process, which is the AR autoregressive model, the MA linear moving averages model, and the ARMA mixed model .Therefore, two methods were used to estimate the spectral density function for the common time series models, which is the autoregressive model - moving media (mixed model), which is the traditional maximum likelihood method for the spectral density function according to the functions of these models and the maximum probability method according to the normal distribution and its function. The two methods were tested using standard mean squares error MAPE (Mean Absolute percentage error) and mean square error (Mean square error) by using Monte Carlo simulation, where random errors were generated by Box-Miller method with default values for the parameters of the studied models ARMA (1,0) and up to the model ARMA (2,2) It is θ₂, θ₁, ∅₂, ∅₁: assuming four sample sizes, which are n₁ = 25, n₂ = 50, n₃ = 100, n₄ = 200, and four values of frequency w = [0.25, 0.3, 0.4, 0.5] represented by the spectrum function, And repeat the experiment 1000 times. The greatest possibility method of normal distribution was better than the approximate greatest possibility method for all sample sizes and for all initial (∅₁) values, as well as for all default (Wi) values. The method of greatest possibility for normal distribution was better for all sample sizes and for all values of (θ_1 ∅_2 θ_1 θ_2) in the case of (Wi = 0.4, 0.5) values are large, but if the values (Wi = 0.25, 0.3) are small, they have a negative effect in terms of efficiency.