Estimating and Forecasting Tax Revenues Using GARCH Family of Models: A Case of Pakistan

Forecasting plays a vital role in effective planning and decision-making for policy formulation across a variety of fields of life. The Nonlinear models such as the GARCH family, including symmetric and asymmetric generalized autoregressive conditional heteroscedastic (GARCH) models with both normal and non-normal innovations are applied in this study to capture the dynamic and asymmetric features of the two tax revenue series, sales Tax and Direct Tax in Pakistan. Additionally, Autoregressive Moving Average (ARMA) model is used as the mean model. The prime objective of this research is to examine the estimating and forecasting performance of ARMA models along GARCH family models, for the monthly tax revenue series in Pakistan, particularly focusing on symmetric GARCH and asymmetric GARCH models (EGARCH, TGARCH, and PARCH). Empirical evidence based on the application of these models to the selected series reveals that the GARCH family models effectively confine the heteroscedasticity, highlighting the strength of these models. In addition, three distributions, normal, Student-t and generalized error distribution are considered for the residuals. Under the normal distribution, ARMA(5,4)-EGARCH(1,1,2) model is selected as the best model based on minimum values of MAE, RMSE, MAPE, and TIC. In the same way, for the Student-t and Generalized Error Distribution, the ARMA(5,4)-EGARCH(1,1,1) and ARMA(5,4)-EGARCH(1,1,3) models are selected as the best forecasting models for the sales tax series. The ARMA(3,3)-EGARCH(1,1,1) model is selected as the best forecasting model based on the minimum values of MAE, RMSE, MAPE, and TIC for the direct tax series assuming a normal distribution. Similarly, the ARMA(3,3)-TGARCH(1,1,1) and ARMA(3,3)-TGARCH(1,1,1) models are selected as the best forecasting models for the direct tax.