We introduce a new approach for modeling the time varying behavior and time series evolution of asset returns co-movements. Here, the co-movement in each period is captured by a trajectory of returns correlation, then a sequence of this over time and the time series evolution are studied. We rely on functional principal components to achieve dimension reduction and to construct the dynamic space of interest, while introducing a new class of information criteria in order to identify the finite dimensionality of the curve time series. Our method is able to combine two of the most applied ideas in the literature, namely economics (or finance) based and time-series based time-varying correlation models. This offers a general specification that is able to model processes of time-varying time-series correlations generated under many existing models that have dominated the financial literature for several decades. To illustrate its empirical relevance, we apply our method to model the time varying co-movement of exchange rate returns for a group of small open economies with large financial sectors. Our empirical results indicate that concepts of time varying correlation enabled by existing methods are too restrictive to accommodate fully the time varying behavior and time series evolution of the returns correlation. On the other hand, our method gives a more complete picture and is able to provide more accurate correlation forecasts.

我们引入了一种新方法，用于对资产收益联动的时变行为和时间序列演变进行建模。在这里，每个时期的联动由收益相关性的轨迹捕获，然后研究其随时间的序列和时间序列的演变。我们依靠功能主成分来实现降维和构建感兴趣的动态空间，同时引入一类新的信息标准来识别曲线时间序列的有限维数。我们的方法能够结合文献中最常用的两种思想，即基于经济学（或金融）和基于时间序列的时变相关模型。这提供了一个通用规范，能够对在几十年来主导金融文献的许多现有模型下生成的随时间变化的时间序列相关性过程进行建模。为了说明其经验相关性，我们应用我们的方法对一组拥有大型金融部门的小型开放经济体的汇率回报随时间变化的联动进行建模。我们的实证结果表明，现有方法启用的时变相关性概念过于严格，无法完全适应收益相关性的时变行为和时间序列演变。另一方面，我们的方法给出了更完整的画面，并能够提供更准确的相关性预测。我们应用我们的方法来模拟一组拥有大型金融部门的小型开放经济体的汇率回报随时间变化的联动。我们的实证结果表明，现有方法启用的时变相关性概念过于严格，无法完全适应收益相关性的时变行为和时间序列演变。另一方面，我们的方法给出了更完整的画面，并能够提供更准确的相关性预测。我们应用我们的方法来模拟一组拥有大型金融部门的小型开放经济体的汇率回报随时间变化的联动。我们的实证结果表明，现有方法启用的时变相关性概念过于严格，无法完全适应收益相关性的时变行为和时间序列演变。另一方面，我们的方法给出了更完整的画面，并能够提供更准确的相关性预测。