Some closed form robust moment‐based estimators for the MEM(1,1)

In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment‐based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi‐maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μ_t of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk.