Antithetic Power Transformation in Monte Carlo Simulation: Correcting Hidden Errors in the Response Variable

Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. The response variable becomes an asynchronous time series. This leads to hidden errors in the response variable. The purpose of this paper is to illustrate how this happens and how it can be corrected. The method is demonstrated for the case of a simple queue for which the time in the system is known exactly from theory. The paper derives the correlation between an exponential random variable and its antithetic counterpart obtained by power transform with an infinitesimal negative exponent.

Automated summary

Monte Carlo simulation is used with uniformly distributed U(0,1) pseudo-random numbers, which may contain some serial correlation. This paper illustrates how this correlation affects the response variable, which becomes an asynchronous time series. It also presents a method to correct this issue by deriving the correlation between an exponential random variable and its antithetic counterpart.