On an $L^2$ norm for stationary ARMA processes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918447734063104 |
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| author | Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand |
| author_facet | Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand |
| contents | We propose an $L^2$ norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process $X_t$, and compute the $L^2$ norm based on its Wold decomposition. As an application of this $L^2$ norm, we derive bounds on the mean square prediction error for AR(1) models of MA(1) processes, and verify these bounds empirically for sample data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_10610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an $L^2$ norm for stationary ARMA processes Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand Machine Learning Probability Methodology 60G10 G.3 We propose an $L^2$ norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process $X_t$, and compute the $L^2$ norm based on its Wold decomposition. As an application of this $L^2$ norm, we derive bounds on the mean square prediction error for AR(1) models of MA(1) processes, and verify these bounds empirically for sample data. |
| title | On an $L^2$ norm for stationary ARMA processes |
| topic | Machine Learning Probability Methodology 60G10 G.3 |
| url | https://arxiv.org/abs/2408.10610 |