Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914504214839296 |
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| author | Dijk, Dylan Cho, Haeran |
| author_facet | Dijk, Dylan Cho, Haeran |
| contents | We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To handle heavy tails, we propose an element-wise data truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2ε)$-th moment only for some $ε\in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $ε$, are comparable to the rates attainable in light-tailed settings as $ε\to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series Dijk, Dylan Cho, Haeran Methodology We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To handle heavy tails, we propose an element-wise data truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2ε)$-th moment only for some $ε\in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $ε$, are comparable to the rates attainable in light-tailed settings as $ε\to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators. |
| title | Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series |
| topic | Methodology |
| url | https://arxiv.org/abs/2509.22235 |