具有重复截面的随机波动率的多水平模型：部落艺术品价格的应用
Multilevel Models with Stochastic Volatility for Repeated Cross-Sections: an Application to tribal Art Prices
摘要：
在本文中，我们介绍了一个多层次的规格与随机波动重复横截面数据。在重复的横截面的时间动态建模需要一个适当的适应的多层次的框架，其中的个人/项目在第一级建模，而时间分量出现在第二级。我们执行极大似然估计通过一个非线性状态空间的方法结合高斯-勒让德积分方法来近似的似然函数。我们将该模型应用于全球最重要的拍卖行出售的部落艺术品的第一个数据库。该模型可以正确地解释所观察到的异方差和自相关波动，并具有优越的预测性能。此外，它还提供了有关市场趋势和价格可预测性的宝贵信息，可供艺术品市场利益相关者使用。
英文摘要：
In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss-Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders.
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