Nonparametric Wavelet-Based Regression Modeling of Oil Revenues and Inflation Incorporating a Hurst Threshold for Irregularly Spaced Economic Data

Abstract

The wavelet shrinkage estimator is considered an attractive technique for estimating nonparametric regression functions due to its high efficiency. However, it suffers from the requirement of a dyadic sample size and the assumption that observations are equally spaced and regularly distributed. When estimation is performed without satisfying these conditions, the resulting estimates are inaccurate.
This study aims to model the relationship between oil revenues and the inflation rate using a nonparametric regression model based on wavelet transforms, employing the Hurst threshold as an adaptive mechanism that reflects the long-memory properties of economic data. The significance of the study stems from the limitations of traditional methods, particularly the universal threshold, in representing irregular time series characterized by temporal dependence, which leads to information loss due to over smoothing   
The study relies on real monthly data for the Iraqi economy over the period from 1/1/2011 to 30/11/2022, comprising (228) observations, This provides a suitable application environment for analyzing the dynamics of a rentier economy that relies heavily on oil revenues. Wavelet smoothing was integrated with threshold adjustment based on the Hurst exponent, allowing the model to adapt to the temporal structure of the series.
The results demonstrated a clear superiority of the Hurst threshold model compared to the general threshold in terms of estimation accuracy, as it achieved a noticeable reduction in both RMSE and MAE, in addition to its ability to preserve the structural characteristics of inflation, as evidenced by the graphical analysis. The findings also revealed that the relationship between oil revenues and inflation is nonlinear and complex, influenced by economic shocks and temporal accumulations.
The study concludes that incorporating long-memory properties within the wavelet regression framework provides a more realistic representation of economic relationships and enhances the efficiency of nonparametric models, particularly in volatile rentier economies such as the Iraqi economy.