Motivated by improving the fitting of non‐negative financial time series, we extend the multiplicative error model and study the semi‐parametric estimation. We first introduce a location parameter and use the sample minimum to a truncate data set. In the case that there is a non‐trivial proportion of zeros in the truncated data, we adopt a zero‐augmented mixture distribution for the innovation terms. For both cases, we propose quasi maximum likelihood estimation for the multiplicative coefficients and establish asymptotic results. We conduct large simulation studies to demonstrate substantial estimation errors with misspecified models, and confirm the asymptotic properties. Moreover, we present an empirical study to illustrate the fitting improvement.

中文翻译：

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具有拟最大似然估计的位置乘法误差模型

通过改进非负金融时间序列的拟合，我们扩展了乘法误差模型并研究了半参数估计。我们首先引入一个位置参数并使用样本最小值来截断数据集。在截断数据中存在非平凡比例的零的情况下，我们对创新项采用零增强混合分布。对于这两种情况，我们建议对乘法系数进行拟最大似然估计并建立渐近结果。我们进行了大型模拟研究，以证明错误指定的模型存在大量估计错误，并确认渐近特性。此外，我们提出了一项实证研究来说明拟合改进。