{"paper":{"title":"A QR Decomposition Approach to Factor Modelling: A Thesis Report","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Immanuel Manohar","submitted_at":"2018-11-27T23:02:19Z","abstract_excerpt":"An observed $K$-dimensional series $\\left\\{ y_{n}\\right\\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\\varepsilon_{n}$ is taken to relate the factors with the observation. The goal is to determine the dimension of the factors, $p$, the factor loading matrix, $Q$, and the factors $f_{n}$. Here, it is assumed that the noise co-variance is positive definite and allowed to be correlated with the factors. An augmented matrix, \\[ \\tilde{M}\\triangleq\\left[\\begin{array}{cccc} \\tilde{\\S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11302","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}