Note on AR(1)-characterisation of stationary processes and model fitting
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance esti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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VTeX
2019-03-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/19-VMSTA132 |
| _version_ | 1819168883888619520 |
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| author | Marko Voutilainen Lauri Viitasaari Pauliina Ilmonen |
| author_facet | Marko Voutilainen Lauri Viitasaari Pauliina Ilmonen |
| author_sort | Marko Voutilainen |
| collection | DOAJ |
| description | It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes. |
| first_indexed | 2024-12-22T19:10:41Z |
| format | Article |
| id | doaj.art-193207670d73412595c9690febdb3300 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-22T19:10:41Z |
| publishDate | 2019-03-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-193207670d73412595c9690febdb33002022-12-21T18:15:40ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542019-03-016219520710.15559/19-VMSTA132Note on AR(1)-characterisation of stationary processes and model fittingMarko Voutilainen0Lauri Viitasaari1Pauliina Ilmonen2Department of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, FinlandDepartment of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, FinlandDepartment of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, FinlandIt was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.https://www.vmsta.org/doi/10.15559/19-VMSTA132AR(1)-characterisationstationary processescovariance functions |
| spellingShingle | Marko Voutilainen Lauri Viitasaari Pauliina Ilmonen Note on AR(1)-characterisation of stationary processes and model fitting Modern Stochastics: Theory and Applications AR(1)-characterisation stationary processes covariance functions |
| title | Note on AR(1)-characterisation of stationary processes and model fitting |
| title_full | Note on AR(1)-characterisation of stationary processes and model fitting |
| title_fullStr | Note on AR(1)-characterisation of stationary processes and model fitting |
| title_full_unstemmed | Note on AR(1)-characterisation of stationary processes and model fitting |
| title_short | Note on AR(1)-characterisation of stationary processes and model fitting |
| title_sort | note on ar 1 characterisation of stationary processes and model fitting |
| topic | AR(1)-characterisation stationary processes covariance functions |
| url | https://www.vmsta.org/doi/10.15559/19-VMSTA132 |
| work_keys_str_mv | AT markovoutilainen noteonar1characterisationofstationaryprocessesandmodelfitting AT lauriviitasaari noteonar1characterisationofstationaryprocessesandmodelfitting AT pauliinailmonen noteonar1characterisationofstationaryprocessesandmodelfitting |