The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of $[0,\pi ]$ radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.

中文翻译：

---

离散和连续时间的线性随机模型

通常将自回归移动平均模型应用于其的计量经济学数据可能包含有限频率范围内的元素。如果数据未涵盖Nyquist的整个频率范围$[0，\pi ]$弧度，则在估计其参数时可能会出现严重偏差。手段应该是重新构造潜在的连续数据轨迹，并以适当的较小速率对其进行重新采样。可以通过将正整数函数核与数据点相关联来得出轨迹。这为基础流程提出了一个模型。本文描述了符合这种模型的有限频率线性随机微分方程，并将其与假定由无界频率的白噪声过程驱动的模型方程进行比较。描述了估计两个品种模型​​的方法。