Asymptotic properties for self-weighted M-estimation of MEM

Introduction In the context of non-negative high-frequency financial time series, the multiplicative error model (MEM) is a generalized model. Maximum Likelihood Estimation (MLE) serves as the standard approach for parameter estimation when applying MEM to real-world modeling. This method relies on the assumption that the error term follows a specific known distribution with finite variance. However, directly imposing the assumption of a known distribution with bounded variance entails notable limitations. Methods In this model, a self-weighted M-estimation approach is used to estimate the model parameters. This estimation is performed considering the infinite variance of the model errors. Results On a theoretical level, this estimation proved to have strong consistency and asymptotic normality. The results of the numerical simulations show that self-weighted M-estimation is more robust than other estimation methods. Finally, the self-weighted M-estimation method is applied to the price range of polyethylene and polypropylene futures on the Dalian Commodity Exchange. Discussion The results demonstrate that the self-weighted M-estimation outperforms both maximum likelihood estimation and least absolute deviation estimation. This finding is particularly significant for financial applications, where extreme outliers and infinite-variance events are frequently observed.