Wasserstein autoregressive models for density time series
Wasserstein autoregressive models for density time series
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DOI：
10.1111/jtsa.12590
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发表时间：
2021-05-07
影响因子：
0.9
通讯作者：
Petersen, Alexander
中科院分区：
文献类型：
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作者：
Zhang, Chao;Kokoszka, Piotr;Petersen, Alexander
由横断面或日内收益的时间索引分布组成的数据在金融领域得到了广泛的研究，并提供了一个由序列相关概率分布组成的数据原子的例子。在这些数据的激励下，我们提出了一个密度时间序列的自回归模型，该模型利用了由Wasserstein度量引起的分布空间上的切空间结构。密度本身不假设有任何特定的参数形式，导致未来未观测密度的灵活预测。序-p Wasserstein自回归模型的主要估计目标是Wasserstein自相关和向量值自回归参数。我们提出了合适的估计量，并建立了它们的渐近正态性，并在仿真研究中得到了验证。新的order-p Wasserstein自回归模型导致了一个预测算法，其中包括一个数据驱动的顺序选择过程。通过对四个财务回报数据集的应用，将其性能与现有的预测程序进行比较，其中使用各种指标来量化预测准确性。对于大多数指标，所提出的模型在两个数据集中优于现有方法，而在其他两个数据集中，基于密度的函数变换的现有方法获得了最佳的经验性能。
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series by exploiting the tangent space structure on the space of distributions that is induced by the Wasserstein metric. The densities themselves are not assumed to have any specific parametric form, leading to flexible forecasting of future unobserved densities. The main estimation targets in the order-p Wasserstein autoregressive model are Wasserstein autocorrelations and the vector-valued autoregressive parameter. We propose suitable estimators and establish their asymptotic normality, which is verified in a simulation study. The new order-p Wasserstein autoregressive model leads to a prediction algorithm, which includes a data driven order selection procedure. Its performance is compared to existing prediction procedures via application to four financial return data sets, where a variety of metrics are used to quantify forecasting accuracy. For most metrics, the proposed model outperforms existing methods in two of the data sets, while the best empirical performance in the other two data sets is attained by existing methods based on functional transformations of the densities.