Estimating mixtures of normal distributions via empirical characteristic function

Abstract

This paper uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions. Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. It is shown that, using Monte Carlo simulation, the finite sample properties of th ECF estimator are very good, even in the case where the popular maximum likelihood estimator fails to exist. An empirical application is illustrated using the monthl excess return of the Nyse value-weighted index.

Keywords:

• constrained Maximum-likelihood;
• empirical characteristic function;
• grid points;
• mixtures of normal distribution
• moment generating function
• Monte Carlo simulation