Estimation in time series analysis aids in making a reasonable decision by providing a value for point estimation and a range of interval estimation. An auto-regressive model is designed for the time series analysis. However, the auto-regressive model may cause decreasing accuracy and prediction in estimating parameters because it uses the assumption that the distribution of error term follows a normal distribution. In reality, there are plenty of data indicating that the distribution of error term does not follow the normal distribution. Thus, we propose a method for solving this problem by using a Pearson distribution system and maximum likelihood estimation. Compared with existing methods, the proposed method can be applied to various time series data requiring high accuracy and prediction.