Abstract
We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix, but infer all spatial interactions from the data. Assuming sparsity, we estimate the spatial and temporal dependence fully data-driven by penalizing a set of Yule–Walker equations. This regularization can be left unstructured, but we also propose customized shrinkage procedures when observations originate from spatial grids (e.g. satellite images). Finite sample error bounds are derived and estimation consistency is established in an asymptotic framework wherein the sample size and the number of spatial units diverge jointly. Exogenous variables can be included as well. A simulation exercise shows strong finite sample performance compared to competing procedures. As an empirical application, we model satellite measured nitrogen dioxide (NO2) concentrations in London. Our approach delivers forecast improvements over a competitive benchmark and we discover evidence for strong spatial interactions.
| Original language | English |
|---|---|
| Article number | 105520 |
| Pages (from-to) | 1-28 |
| Number of pages | 28 |
| Journal | Journal of Econometrics |
| Volume | 239 |
| Issue number | 1 |
| Early online date | 21 Oct 2023 |
| DOIs | |
| Publication status | Published - Feb 2024 |
Bibliographical note
Funding Information:This paper (or earlier versions hereof) has been presented during the internal seminar of the Quantitative Economics department of Maastricht University, the Econometrics Internal Seminar (EIS) at Erasmus University Rotterdam, the Bernoulli-IMS One World Symposium, the workshop on Dimensionality Reduction and Inference in High-dimensional Time Series at Maastricht University, the 2021 Annual Conference of the International Association for Applied Econometrics (IAAE), the 5th Conference on Econometric Models of Climate Change, the internal seminar at Tor Vergata University of Rome, and the 2021 (EC)2 Conference. We gratefully acknowledge comments and feedback from the participants. Suggestions by Stephan Smeekes and Ines Wilms were particularly helpful, so we thank them explicitly. In addition, we thank the two anonymous referees for their constructive feedback that has resulted in major improvements in our work. All remaining errors are our own.
Publisher Copyright:
© 2023 The Author(s)
Funding
This paper (or earlier versions hereof) has been presented during the internal seminar of the Quantitative Economics department of Maastricht University, the Econometrics Internal Seminar (EIS) at Erasmus University Rotterdam, the Bernoulli-IMS One World Symposium, the workshop on Dimensionality Reduction and Inference in High-dimensional Time Series at Maastricht University, the 2021 Annual Conference of the International Association for Applied Econometrics (IAAE), the 5th Conference on Econometric Models of Climate Change, the internal seminar at Tor Vergata University of Rome, and the 2021 (EC)2 Conference. We gratefully acknowledge comments and feedback from the participants. Suggestions by Stephan Smeekes and Ines Wilms were particularly helpful, so we thank them explicitly. In addition, we thank the two anonymous referees for their constructive feedback that has resulted in major improvements in our work. All remaining errors are our own.
Keywords
- High-dimensional
- Satellite data
- Spatio-temporal models
- SPLASH
- Yule–Walker
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