Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes
High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process ( Y n Δ ) n ∈ Z as Δ ↓ 0 , where ( Y t ) t ∈ R is an MCARMA process. We show that the properly filtered...
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| Veröffentlicht in: | Annals of the Institute of Statistical Mathematics 2018-04, Vol.70 (2), p.467-487 |
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| container_title | Annals of the Institute of Statistical Mathematics |
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| creator | Kevei, Péter |
| description | High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process
(
Y
n
Δ
)
n
∈
Z
as
Δ
↓
0
, where
(
Y
t
)
t
∈
R
is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive
Δ
. However, the results established here provide a useful and insightful approximation when
Δ
is very small. |
| doi_str_mv | 10.1007/s10463-017-0601-5 |
| format | Article |
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(
Y
n
Δ
)
n
∈
Z
as
Δ
↓
0
, where
(
Y
t
)
t
∈
R
is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive
Δ
. However, the results established here provide a useful and insightful approximation when
Δ
is very small.</description><identifier>ISSN: 0020-3157</identifier><identifier>EISSN: 1572-9052</identifier><identifier>DOI: 10.1007/s10463-017-0601-5</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Approximation ; Asymptotic properties ; Asymptotic series ; Autoregressive moving average ; Autoregressive processes ; Economics ; Eigenvalues ; Finance ; Insurance ; Investigations ; Management ; Mathematics ; Mathematics and Statistics ; Parameter estimation ; Representations ; Statistics ; Statistics for Business</subject><ispartof>Annals of the Institute of Statistical Mathematics, 2018-04, Vol.70 (2), p.467-487</ispartof><rights>The Institute of Statistical Mathematics, Tokyo 2017</rights><rights>Annals of the Institute of Statistical Mathematics is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-38c11c11c5148d62239a5ea4f5674a0a2541834df31c36aaf4952010900634ea3</citedby><cites>FETCH-LOGICAL-c316t-38c11c11c5148d62239a5ea4f5674a0a2541834df31c36aaf4952010900634ea3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10463-017-0601-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10463-017-0601-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Kevei, Péter</creatorcontrib><title>Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes</title><title>Annals of the Institute of Statistical Mathematics</title><addtitle>Ann Inst Stat Math</addtitle><description>High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process
(
Y
n
Δ
)
n
∈
Z
as
Δ
↓
0
, where
(
Y
t
)
t
∈
R
is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive
Δ
. However, the results established here provide a useful and insightful approximation when
Δ
is very small.</description><subject>Approximation</subject><subject>Asymptotic properties</subject><subject>Asymptotic series</subject><subject>Autoregressive moving average</subject><subject>Autoregressive processes</subject><subject>Economics</subject><subject>Eigenvalues</subject><subject>Finance</subject><subject>Insurance</subject><subject>Investigations</subject><subject>Management</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Parameter estimation</subject><subject>Representations</subject><subject>Statistics</subject><subject>Statistics for 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moving average representation of high-frequency sampled multivariate CARMA processes</title><author>Kevei, Péter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-38c11c11c5148d62239a5ea4f5674a0a2541834df31c36aaf4952010900634ea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Approximation</topic><topic>Asymptotic properties</topic><topic>Asymptotic series</topic><topic>Autoregressive moving average</topic><topic>Autoregressive processes</topic><topic>Economics</topic><topic>Eigenvalues</topic><topic>Finance</topic><topic>Insurance</topic><topic>Investigations</topic><topic>Management</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Parameter estimation</topic><topic>Representations</topic><topic>Statistics</topic><topic>Statistics for 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moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process
(
Y
n
Δ
)
n
∈
Z
as
Δ
↓
0
, where
(
Y
t
)
t
∈
R
is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive
Δ
. However, the results established here provide a useful and insightful approximation when
Δ
is very small.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s10463-017-0601-5</doi><tpages>21</tpages></addata></record> |
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| ispartof | Annals of the Institute of Statistical Mathematics, 2018-04, Vol.70 (2), p.467-487 |
| issn | 0020-3157 1572-9052 |
| language | eng |
| recordid | cdi_proquest_journals_2008300930 |
| source | Springer Nature - Complete Springer Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Approximation Asymptotic properties Asymptotic series Autoregressive moving average Autoregressive processes Economics Eigenvalues Finance Insurance Investigations Management Mathematics Mathematics and Statistics Parameter estimation Representations Statistics Statistics for Business |
| title | Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes |
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