Noncausality in Continuous Time Models
研究了连续时间框架下非因果性的新定义，以随机波动率模型为例，定义了CIMA过程并给出参数化特征，探讨了连续与离散时间定义的联系及混叠问题，为结构解释和检验提供基础。
In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.