Order 1 autoregressive process of finite length
The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in time series theory one analyzes only stochastic processes of in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2007-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/869 |
| _version_ | 1828541817554993152 |
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| author | Călin Vamoş Ştefan M. Şoltuz Maria Crăciun |
| author_facet | Călin Vamoş Ştefan M. Şoltuz Maria Crăciun |
| author_sort | Călin Vamoş |
| collection | DOAJ |
| description | The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in time series theory one analyzes only stochastic processes of infinite length which need no such initial conditions and their properties are less difficult to be determined. In this paper we compare the properties of the order 1 autoregressive processes of finite and infinite length and we prove that the time series length has an important influence mainly if the serial correlation is significant. These different properties can manifest themselves as transient effects produced when a time series is numerically generated. We show that for an order 1 autoregressive process the transient behavior can be avoided if the first term is a Gaussian random variable with standard deviation equal to that of the theoretical infinite process and not to that of the white noise innovation. |
| first_indexed | 2024-12-12T01:45:44Z |
| format | Article |
| id | doaj.art-776ff0396bd244c7b5285c162def98b2 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T01:45:44Z |
| publishDate | 2007-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-776ff0396bd244c7b5285c162def98b22022-12-22T00:42:35ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2007-08-01362Order 1 autoregressive process of finite lengthCălin Vamoş0Ştefan M. Şoltuz1Maria Crăciun2Tiberiu Popoviciu Institute of Numerical Analysis, Romanian AcademyTiberiu Popoviciu Institute of Numerical Analysis, Romanian AcademyTiberiu Popoviciu Institute of Numerical Analysis, Romanian AcademyThe stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in time series theory one analyzes only stochastic processes of infinite length which need no such initial conditions and their properties are less difficult to be determined. In this paper we compare the properties of the order 1 autoregressive processes of finite and infinite length and we prove that the time series length has an important influence mainly if the serial correlation is significant. These different properties can manifest themselves as transient effects produced when a time series is numerically generated. We show that for an order 1 autoregressive process the transient behavior can be avoided if the first term is a Gaussian random variable with standard deviation equal to that of the theoretical infinite process and not to that of the white noise innovation.https://www.ictp.acad.ro/jnaat/journal/article/view/869autoregressive processspectral analysistime series |
| spellingShingle | Călin Vamoş Ştefan M. Şoltuz Maria Crăciun Order 1 autoregressive process of finite length Journal of Numerical Analysis and Approximation Theory autoregressive process spectral analysis time series |
| title | Order 1 autoregressive process of finite length |
| title_full | Order 1 autoregressive process of finite length |
| title_fullStr | Order 1 autoregressive process of finite length |
| title_full_unstemmed | Order 1 autoregressive process of finite length |
| title_short | Order 1 autoregressive process of finite length |
| title_sort | order 1 autoregressive process of finite length |
| topic | autoregressive process spectral analysis time series |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/869 |
| work_keys_str_mv | AT calinvamos order1autoregressiveprocessoffinitelength AT stefanmsoltuz order1autoregressiveprocessoffinitelength AT mariacraciun order1autoregressiveprocessoffinitelength |