Working Paper: CEPR ID: DP17091
Authors: Martin Lettau
Abstract: This paper considers extensions of 2-dimensional factor models to higher-dimension data that can be represented as tensors. I describe decompositions of tensors that generalize the standard matrix singular value decomposition and principal component analysis to higher dimensions. I estimate the model using a 3-dimensional data set consisting of 25 characteristics of 1,342 mutual funds observed over 34 quarters. The tensor factor models reduce the data dimensionality by 97% while capturing 93% of the variation of the data. I relate higher-dimensional tensor models to standard 2-dimensional model and show that the components of the model have clear economic interpretations.
Keywords: Tucker Decomposition; CP Decomposition; Tensors; PCA; SVD; Factor Models; Mutual Funds; Characteristics
JEL Codes: G12; G38
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| tensor factor models (C38) | efficiency of data representation (C55) |