Forecasting in the presence of scale-free noise
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914293046312960 |
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| author | Kryhin, Serhii Mouzykantskii, Tatiana Sudhir, Vivishek |
| author_facet | Kryhin, Serhii Mouzykantskii, Tatiana Sudhir, Vivishek |
| contents | The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past observations. Current techniques for deriving the filter require that the noise be well described by rational power spectra. However, scale-free noises, whose spectra scale as a non-integer power of frequency, are ubiquitous in practice. We establish a method, together with performance guarantees, that solves the forecasting problem in the presence of scale-free noise. Via the duality between estimation and control, our technique can be used to design control for distributed systems. These results will have wide-ranging applications in neuroscience, finance, fluid dynamics, and quantum measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forecasting in the presence of scale-free noise Kryhin, Serhii Mouzykantskii, Tatiana Sudhir, Vivishek Optimization and Control Systems and Control Signal Processing The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past observations. Current techniques for deriving the filter require that the noise be well described by rational power spectra. However, scale-free noises, whose spectra scale as a non-integer power of frequency, are ubiquitous in practice. We establish a method, together with performance guarantees, that solves the forecasting problem in the presence of scale-free noise. Via the duality between estimation and control, our technique can be used to design control for distributed systems. These results will have wide-ranging applications in neuroscience, finance, fluid dynamics, and quantum measurements. |
| title | Forecasting in the presence of scale-free noise |
| topic | Optimization and Control Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2601.22294 |