Location Multiplicative Error Models with Quasi Maximum Likelihood Estimation

Abstract

Motivated by improving the fitting of non‐negative financial time series, we extend the multiplicative error model and study the semi‐parametric estimation. We first introduce a location parameter and use the sample minimum to a truncate data set. In the case that there is a non‐trivial proportion of zeros in the truncated data, we adopt a zero‐augmented mixture distribution for the innovation terms. For both cases, we propose quasi maximum likelihood estimation for the multiplicative coefficients and establish asymptotic results. We conduct large simulation studies to demonstrate substantial estimation errors with misspecified models, and confirm the asymptotic properties. Moreover, we present an empirical study to illustrate the fitting improvement.