We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.

翻译：本文针对一类广泛的半参数时间序列模型提出了一种新的估计方法，其中条件期望通过参数化函数建模。所提出的估计量类别基于高斯拟似然函数，并依赖于一个包含关于条件期望的参数约束的伪方差设定。在观测驱动模型中，当可观测过程的支撑集存在边界（如计数过程和双有界时间序列）时，伪方差与参数约束的设定自然成立。我们推导了估计量的渐近性质，并给出了参数约束的有效性检验。结果表明，无论伪方差的设定是否正确，相关结论均保持有效。相较于文献中已有的其他拟似然方法，约束估计量的核心优势在于其能实现更高的效率。此外，该检验方法可用于构建参数时间序列模型的设定检验。我们通过仿真研究以及两个实证应用展示了该方法在实践中的用途：其一涉及整数值自回归过程（对稀疏算子的离散性假设进行了正式检验），其二涉及双有界数据的自回归模型（应用于已实现相关系数时间序列）。