<b>Autoregressive Models Estimation Selection with Known Marginal Distribution</b>

A time series is a sequence of observations recorded at regular intervals. Time series analysis has applications in diverse fields such as finance, stock prices, economics, environmental science, and social network data analysis. The recorded series is used to represent a measurable quantity or attribute, such as temperature readings, economic indicators, or other variables, depending on the context of the analysis. The idea of time series analysis is to identify patterns, trends, or underlying structures within the data, as well as to make predictions or forecasts about future values based on previous observations. Autoregressive (AR) models are widely used in modeling and forecasting data from time series. This work focuses on AR model parameter estimation, emphasizing the significance of the likelihood function by defining the marginal distribution of the AR process, which is getting by representing the AR process with random shocks and assuming the error terms in a time series have a normal distribution with a zero mean and variance . Some of the simulated experiments are designed to fit the model for different model orders and sample size to find model parameter estimation by likelihood function with marginal distribution. The results of Mean Squares Errors (MSE) and Mean Percentage Errors (MPE) indicate the significance and robust estimation of the AR –models parameters estimators that are computed theoretically.