180 – High-Frequency and Other Financial Econometric Topics
Modi fied QMLEs for Location and Zero-Augmented Multiplicative Error Models: Order of (1,1)
Qian Li
University of Kansas Medical Center
We extend the linear Multiplicative Error Model (MEM) at order of (1,1) by adding the location parameter. The minimum of the sample is shown to be a consistent estimator for this parameter, and used to truncate the data set. If the truncated data set contains none or a trivial proportion of zeros, the remaining coefficients are estimated by the Gaussian Quasi Maximum Likelihood Estimator (QMLE). If a large proportion of zeros exist in the truncated data set, we adopt a Zero-Augmented (ZA) distribution for the random errors in MEM and propose a modified QMLE (ZA-QMLE) without specifying the continuous density to estimate the coefficients in this ZA model. Consistency and asymptotic normality are discussed for both estimators under mild assumptions at order of (1,1). We also conduct simulation studies at both (1,1) and higher orders and empirical analysis on IBM High Frequency trading data, to illustrate the asymptotic results and model improvement for both cases.