Generating Halton Sequences using Mata

Abstract

This paper discusses the advantages of Halton sequences over pseudorandom uniform numbers when using simulation to approximate integrals numerically. We describe two types of sequences and give Mata examples. Finally, we document the Mata function halton(), currently in release 9.1 of Stata, which computes both a Halton sequence and its Hammersley variant. Options to use these point sets are available in the Stata 9 program asmprobit, a multinomial-probit estimator, and in the Stata 9.1 Mata function ghk(), the Geweke–Hajivassiliou–Keane multivariate-normal simulator.