In economic and business data, the correlation matrix is a stochastic process that fluctuates over time and exhibits seasonality. The most widely-used approaches for estimating and forecasting the correlation matrix (e.g., multivariate GARCH) often are hindered by computational difficulties and require strong assumptions. In this paper we propose a method for modeling and forecasting correlation matrices that allows the correlation to be driven nonlinearly by common factors. Our nonlinear common factor (NCF) method simplifies estimation and provides more flexibility than previous factor-based methods. We illustrate its use on energy prices in Boston.

在经济和商业数据中，相关矩阵是随时间波动并表现出季节性的随机过程。用于估计和预测相关矩阵的最广泛使用的方法（例如，多元GARCH）通常会受到计算困难的阻碍，并且需要强有力的假设。在本文中，我们提出了一种用于建模和预测相关矩阵的方法，该方法允许相关性由公因子非线性驱动。与以前的基于因子的方法相比，我们的非线性公共因子（NCF）方法简化了估算并提供了更大的灵活性。我们说明了其在波士顿能源价格中的用途。