Efficient Initialization of the Correlation Matrix in NORTA Using Quasi-Monte Carlo and Updating Techniques

Simulating multivariate random variables is essential in data analytics as it allows for more accurate modeling, improved decision-making, and a better understanding of complex systems and processes. The NORTA algorithm, a widely used method, can accomplish this task. However, it requires an initial correlation matrix to produce multivariate random variables with the desired correlation matrix, and both matrices usually differ. This paper presents an efficient simulation-based algorithm for determining the initial correlation matrix, leveraging quasi-Monte Carlo integration with the Halton sequence, an adaptive sum of squared errors, and some probability distributions. The proposed algorithm is tested to generate many cases of multivariate random variables with different distributions and different correlation matrices. The results show that this algorithm can substantially reduce time compared to the traditional simulation-based method.