The intervals between successive trades on the stock exchange, market activity, number of trades, financial market volatility, queue waiting times, squared log-returns, and power demand are certain time series restricted to non-negative values. The multiplicative error model (MEM) has gained traction as a preferred method for analyzing non-negative data sets. This article specifically introduces the MEM, where the errors are derived from a two-component mixture distribution. Mixture distributions are applied to model random phenomena, effectively addressing the multimodal, asymmetric, and skewed characteristics. The study also considers both classical and robust estimation methods utilizing the expectation-maximization (EM) algorithm. In conjunction with the EM estimates, we additionally introduce two robust estimators tailored for the MEM, called the EM-type M-estimates and EM-type BM-estimates. The results of the Monte Carlo simulation reveal that the robust estimators exhibit good performance irrespective of the presence of outliers, with the EM-type BM-estimates demonstrating superior robustness and diminished susceptibility to outliers compared to alternative estimation methodologies. Finally, the proposed methodology is effectively employed to model the monthly equity market volatility tracker (EMVT) series, supported by goodness-of-fit measures that substantiate the applicability of the proposed approach. The empirical application demonstrates that the EM-type BM-estimates have a better forecasting capacity.
Farahabadi et al. (Mon,) studied this question.