Maintaining Prior Distributions across Evolving Eigenspaces: An Application to Portfolio Construction

Temporal evolution in the generative distribution of nonstationary sequential data is challenging to model. This paper presents a method for retaining the information in prior distributions of matrix variate dynamic linear models (MVDLMs) as the eigenspace of sequential data evolves. The method starts by constructing sliding windows â" matrices composed of a fixed number of columns containing the most recent point-in-time multivariate observation vectors. Characteristic time series, the right singular vectors, are extracted from a window using singular value decomposition (SVD). Then, a sequence of matrices capturing the rotation and scaling of the eigenspace is specified as a function of adjacent windowsâ characteristic time series. The method is tested on observations derived from daily US stock prices spanning 25 years. The results indicate that models constructed using sliding window SVD and MVDLMs, as extended in this paper, are resistant to over-fitting and perform well when used in portfolio construction applications.