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The autoregressive model is a representation of a certain kind of random process in statistics, insurance, signal processing, and econometrics; as such, it is used to describe some time-varying processes in nature, economics and insurance, etc. In this article, a novel version of the autoregressive model is proposed, in the so-called the partially autoregressive (PAR(1)) model. The results of the new approach depended on a new algorithm that we formulated to facilitate the process of statistical prediction in light of the rapid developments in time series models. The new algorithm is based on the values of the autocorrelation and partial autocorrelation functions. The new technique is assessed via re-estimating the actual time series values. Finally, the results of the PAR(1) model is compared with the Holt-Winters model under the Ljung-Box test and its corresponding p-value. A comprehensive analysis for the model residuals is presented. The matrix of the autocorrelation analysis for both points forecasting and interval forecasting are given with its relevant plots.


Time series Statistical model Forecasting Residual analysis Ljung-Box test Simulation Statistics and Numerical Data

Article Details

Author Biographies

Salwa L. Alkhayyat, Department of Statistics, Faculty of Science, University of Jeddah, Kingdom of Saudi Arabia

Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Kafr El-Sheikh University, Egypt

Emadeldin I. A. Ali, Department of Economics, College of Economics and Administrative Sciences, Al Imam Mohammad Ibn Saud Islamic University, Saudi Arabia

Department of Mathematics, Statistics, and Insurance, Faculty of Business, Ain Shams University, Egypt

How to Cite
Alkhayyat, S. L., Mohamed, H. S., Butt, N. S., Yousof, H. M., & Ali, E. I. A. (2023). Modeling the Asymmetric Reinsurance Revenues Data using the Partially Autoregressive Time Series Model: Statistical Forecasting and Residuals Analysis. Pakistan Journal of Statistics and Operation Research, 19(3), 425-446.

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