Nonlinear and nonnormal filter using importance sampling: Antithetic Monte Carlo integration

In this paper, the importance sampling filter proposed by Mariano and Tanizaki (1995). Tanizaki (1996), Tanizaki and Mariano (1994) is extended using the antithetic Monte Carlo method to reduce the simulation errors. By;Monte Carlo studies, the importance sampling filter with the antithetic Monte Carlo method is compared with the importance sampling filter without the antithetic Monte Carlo method. It is shown that for all the simulation studies the former is clearly superior to the latter especially when number of random draws is small.