Working Paper: NBER ID: w29833
Authors: Martin Lettau
Abstract: This paper considers extensions of two-dimensional factor models to higher-dimensional data 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 three-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 two-dimensional models and show that the components of the model have clear economic interpretations.
Keywords: Factor Models; Mutual Funds; High-Dimensional Data
JEL Codes: C38; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Higher-dimensional tensor models (C31) | Effective summarization of data (Y10) |
| Tensor factor models (C32) | Estimation of factors across multiple characteristics and funds (C38) |
| Core tensor in decomposition (C10) | Contains representative observations (C90) |
| First factors along three dimensions (C38) | Level factors with positive long-only loadings (G19) |
| Higher-order components (Y80) | Long-short factors (G41) |