Factor Models With Sparse Vector Autoregressive Idiosyncratic Components
(2025) In Oxford Bulletin of Economics and Statistics 87(4). p.837-849- Abstract
- We reconcile dense and sparse modelling by exploiting the positive aspects of both. We employ a high-dimensional, approximate static factor model and assume the idiosyncratic term follows a sparse vector autoregressive model (VAR). The estimation is articulated in two steps: (i) factors and loadings are estimated via principal component analysis (PCA); (ii) a sparse VAR is estimated via the lasso on the estimated idiosyncratic components from (i). Step (ii) allows to model cross-sectional and time dependence left after the factors estimation. We prove the consistency of this approach as the time and cross-sectional dimensions diverge. In (ii), sparsity is allowed to be very general: approximate, row-wise, and growing with the sample size.... (More)
- We reconcile dense and sparse modelling by exploiting the positive aspects of both. We employ a high-dimensional, approximate static factor model and assume the idiosyncratic term follows a sparse vector autoregressive model (VAR). The estimation is articulated in two steps: (i) factors and loadings are estimated via principal component analysis (PCA); (ii) a sparse VAR is estimated via the lasso on the estimated idiosyncratic components from (i). Step (ii) allows to model cross-sectional and time dependence left after the factors estimation. We prove the consistency of this approach as the time and cross-sectional dimensions diverge. In (ii), sparsity is allowed to be very general: approximate, row-wise, and growing with the sample size. However, the estimation error of (i) needs to be accounted for. Instead of simply plugging-in the standard rates derived for the PCA estimation of the factors in (i), we derive a refined expression of the error, which enables us to derive tighter rates for the lasso in (ii). We discuss applications on forecasting & factor-augmented regression and present an empirical application on macroeconomic forecasting using the Federal Reserve Economic Data - Monthly Database (FRED-MD). (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3782d5cf-f3fe-4521-b3d9-261f7e96d614
- author
- Krampe, Jonas and Margaritella, Luca LU
- organization
- publishing date
- 2025-02-19
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Oxford Bulletin of Economics and Statistics
- volume
- 87
- issue
- 4
- pages
- 837 - 849
- publisher
- Wiley-Blackwell
- external identifiers
-
- scopus:85217891812
- ISSN
- 1468-0084
- DOI
- 10.1111/obes.12664
- language
- English
- LU publication?
- yes
- id
- 3782d5cf-f3fe-4521-b3d9-261f7e96d614
- date added to LUP
- 2025-02-19 14:55:23
- date last changed
- 2025-08-04 11:46:10
@article{3782d5cf-f3fe-4521-b3d9-261f7e96d614,
abstract = {{We reconcile dense and sparse modelling by exploiting the positive aspects of both. We employ a high-dimensional, approximate static factor model and assume the idiosyncratic term follows a sparse vector autoregressive model (VAR). The estimation is articulated in two steps: (i) factors and loadings are estimated via principal component analysis (PCA); (ii) a sparse VAR is estimated via the lasso on the estimated idiosyncratic components from (i). Step (ii) allows to model cross-sectional and time dependence left after the factors estimation. We prove the consistency of this approach as the time and cross-sectional dimensions diverge. In (ii), sparsity is allowed to be very general: approximate, row-wise, and growing with the sample size. However, the estimation error of (i) needs to be accounted for. Instead of simply plugging-in the standard rates derived for the PCA estimation of the factors in (i), we derive a refined expression of the error, which enables us to derive tighter rates for the lasso in (ii). We discuss applications on forecasting & factor-augmented regression and present an empirical application on macroeconomic forecasting using the Federal Reserve Economic Data - Monthly Database (FRED-MD).}},
author = {{Krampe, Jonas and Margaritella, Luca}},
issn = {{1468-0084}},
language = {{eng}},
month = {{02}},
number = {{4}},
pages = {{837--849}},
publisher = {{Wiley-Blackwell}},
series = {{Oxford Bulletin of Economics and Statistics}},
title = {{Factor Models With Sparse Vector Autoregressive Idiosyncratic Components}},
url = {{http://dx.doi.org/10.1111/obes.12664}},
doi = {{10.1111/obes.12664}},
volume = {{87}},
year = {{2025}},
}