Regression Models with ARMA Errors for Predicting Tabarru Fund in Islamic Insurance: A Normally Distributed Simulation Approach

Abstract

Islamic insurance is a financial protection system based on mutual assistance and risk-sharing, facilitated by a tabarru fund among participants. Effective management of this fund is essential to prevent financial deficits while ensuring sustainability and compliance with Sharia principles. This study aims to predict the value of the tabarru fund by developing a regression model with ARMA errors, incorporating variables such as participant contributions, claim amounts, and investment returns. The Regression model with ARMA errors is a hybrid approach that combines multiple linear regression with ARMA-based residual modeling, effectively addressing autocorrelation in regression residuals. The data used in this study were generated through a normal distribution simulation based on the monthly financial records of a Sharia insurance company over a ten-year period. The analysis results indicated that the regression model with ARMA(1,0) errors could provide predictive values with minimum error of prediction (MAPE value 0.022%). These findings demonstrate the model’s potential for strategic financial planning in Islamic insurance institutions, particularly in optimizing fund allocation and supporting risk-sensitive investment decisions.