A closed-form moment estimator for the vector multiplicative error model and its application

Abstract

The vector multiplicative error model (vMEM) is a popular model known for its capability of analyzing and forecasting multidimensional non-negative-valued time series. In this paper, we present a closed-form estimator for the vMEM. The estimator has the advantage that it can be easily implemented by solving moment equations and does not require the use of any distribution or optimal weight matrix. We prove consistency and derive the asymptotic properties of the estimator. A simulation study confirms our theoretical results and compares the performance of the closed-form estimator (CLFE) and the quasi-maximum likelihood estimator (QMLE). Empirical application of the absolute return and the high–low range from GE stock illustrates the predictive capacity comparison of the CLFE and the QMLE.

Keywords:

• Vector multiplicative error model
• closed-form estimator
• quasi-maximum likelihood estimator
• asymptotic property
• moment equation