A first-order autoregressive process with weighted Lindley innovations and its applications to energy and financial data

This paper presents an autoregressive process of order one in which the innovation term follows a weighted Lindley distribution. The fundamental characteristics of this process are carefully examined. The proposed process is applied to analyze time series data, using real-world datasets. The parameters of the considered model are estimated using the Gaussian estimation approach, and the study offers a comparison of the suggested model with some alternative models in the literature. Moreover, this study investigates data forecasting for the proposed model by applying the classical conditional expectation method alongside some machine learning algorithms to evaluate the prediction accuracy.