Estimate a nonparametric copula density function based on probit and wavelet transforms

Abstract

This study employs wavelet transforms to address the issue of boundary effects. Additionally, it utilizes probit transform techniques, which are based on probit functions, to estimate the copula density function. This estimation is dependent on the empirical distribution function of the variables. The density is estimated within a transformed domain. Recent research indicates that the early implementations of this strategy may have been more efficient. Nevertheless, in this work, we implemented two novel methodologies utilizing probit transform and wavelet transform. We then proceeded to evaluate and contrast these methodologies using three specific criteria: root mean square error (RMSE), Akaike information criterion (AIC), and log-likelihood (LogL). The wavelet transform method works better than the probit transform method at all three levels of correlation, as shown by a simulated study with four types of copulas, five sample sizes, and three levels of correlation. Research has demonstrated that probit transformation methods are most appropriate for linkages involving large and medium sample sizes, as indicated by Frank, Joe, and Tawn Copula. On the other hand, for copula functions for all sample sizes, the wavelet transform method was found to be ideal in cases with low correlation values