Time series aggregation, disaggregation and long memory
Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Cas...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-09-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/30723 |
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| _version_ | 1825197212237299712 |
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| author | Dmitrij Celov Remigijus Leipus |
| author_facet | Dmitrij Celov Remigijus Leipus |
| author_sort | Dmitrij Celov |
| collection | DOAJ |
| description |
Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Castelle and Oppenheim (2001) explored the topic further, answering when and if a predefined long memory process could be obtained as the result of aggregation of a specific class of individual processes. In this paper, the disaggregation scheme of Leipus et al. (2006) is briefly discussed. Then disaggregation into AR(1) is analyzed further, resulting in a theorem that helps, under corresponding assumptions, to construct a mixture density for a given aggregated by AR(1) scheme process. Finally the theorem is illustrated by FARUMA mixture densityÆs example.
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| format | Article |
| id | doaj-art-00ca1a31b3864e679b828dd0db2c5e63 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-00ca1a31b3864e679b828dd0db2c5e632025-02-11T18:12:39ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2023-09-0146spec.10.15388/LMR.2006.30723Time series aggregation, disaggregation and long memoryDmitrij Celov0Remigijus Leipus1Vilnius UniversityVilnius University Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Castelle and Oppenheim (2001) explored the topic further, answering when and if a predefined long memory process could be obtained as the result of aggregation of a specific class of individual processes. In this paper, the disaggregation scheme of Leipus et al. (2006) is briefly discussed. Then disaggregation into AR(1) is analyzed further, resulting in a theorem that helps, under corresponding assumptions, to construct a mixture density for a given aggregated by AR(1) scheme process. Finally the theorem is illustrated by FARUMA mixture densityÆs example. https://www.zurnalai.vu.lt/LMR/article/view/30723mixture densitydisaggregationAR(1) aggregationlong memory |
| spellingShingle | Dmitrij Celov Remigijus Leipus Time series aggregation, disaggregation and long memory Lietuvos Matematikos Rinkinys mixture density disaggregation AR(1) aggregation long memory |
| title | Time series aggregation, disaggregation and long memory |
| title_full | Time series aggregation, disaggregation and long memory |
| title_fullStr | Time series aggregation, disaggregation and long memory |
| title_full_unstemmed | Time series aggregation, disaggregation and long memory |
| title_short | Time series aggregation, disaggregation and long memory |
| title_sort | time series aggregation disaggregation and long memory |
| topic | mixture density disaggregation AR(1) aggregation long memory |
| url | https://www.zurnalai.vu.lt/LMR/article/view/30723 |
| work_keys_str_mv | AT dmitrijcelov timeseriesaggregationdisaggregationandlongmemory AT remigijusleipus timeseriesaggregationdisaggregationandlongmemory |