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ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES
We study the prediction problem for deterministic stationary processes X ( t ) possessing spectral density f . We describe the asymptotic behavior of the best linear mean squared prediction error σ n 2 ( f ) in predicting X ( 0 ) given X ( t ) , - n ≤ t ≤ - 1 , as n goes to infinity. We consider a c...
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Published in: | Acta mathematica Hungarica 2022-08, Vol.167 (2), p.501-528 |
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container_end_page | 528 |
container_issue | 2 |
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container_title | Acta mathematica Hungarica |
container_volume | 167 |
creator | BABAYAN, N. GINOVYAN, M. |
description | We study the prediction problem for deterministic stationary processes
X
(
t
)
possessing spectral density
f
. We describe the asymptotic behavior of the best linear mean squared prediction error
σ
n
2
(
f
)
in predicting
X
(
0
)
given
X
(
t
)
,
-
n
≤
t
≤
-
1
, as
n
goes to infinity. We consider a class of spectral densities of the form
f
=
f
d
g
, where
f
d
is the spectral density of a deterministic process that has a very high order contact with zero due to which the Szegő condition is violated, while
g
is a nonnegative function that can have arbitrary power type singularities. We show that for spectral densities
f
from this class the prediction error
σ
n
2
(
f
)
behaves like a power as
n
→
∞
. Examples illustrate the obtained results. |
doi_str_mv | 10.1007/s10474-022-01248-9 |
format | article |
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X
(
t
)
possessing spectral density
f
. We describe the asymptotic behavior of the best linear mean squared prediction error
σ
n
2
(
f
)
in predicting
X
(
0
)
given
X
(
t
)
,
-
n
≤
t
≤
-
1
, as
n
goes to infinity. We consider a class of spectral densities of the form
f
=
f
d
g
, where
f
d
is the spectral density of a deterministic process that has a very high order contact with zero due to which the Szegő condition is violated, while
g
is a nonnegative function that can have arbitrary power type singularities. We show that for spectral densities
f
from this class the prediction error
σ
n
2
(
f
)
behaves like a power as
n
→
∞
. Examples illustrate the obtained results.</description><identifier>ISSN: 0236-5294</identifier><identifier>EISSN: 1588-2632</identifier><identifier>DOI: 10.1007/s10474-022-01248-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Asymptotic properties ; Density ; Mathematics ; Mathematics and Statistics ; Predictions ; Stationary processes</subject><ispartof>Acta mathematica Hungarica, 2022-08, Vol.167 (2), p.501-528</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2022</rights><rights>Akadémiai Kiadó, Budapest, Hungary 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-2885fc2591c4a52728c4a6f8f6fe851a8acc7c89aa861d69095931374d112ecb3</citedby><cites>FETCH-LOGICAL-c319t-2885fc2591c4a52728c4a6f8f6fe851a8acc7c89aa861d69095931374d112ecb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,786,790,27957,27958</link.rule.ids></links><search><creatorcontrib>BABAYAN, N.</creatorcontrib><creatorcontrib>GINOVYAN, M.</creatorcontrib><title>ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES</title><title>Acta mathematica Hungarica</title><addtitle>Acta Math. Hungar</addtitle><description>We study the prediction problem for deterministic stationary processes
X
(
t
)
possessing spectral density
f
. We describe the asymptotic behavior of the best linear mean squared prediction error
σ
n
2
(
f
)
in predicting
X
(
0
)
given
X
(
t
)
,
-
n
≤
t
≤
-
1
, as
n
goes to infinity. We consider a class of spectral densities of the form
f
=
f
d
g
, where
f
d
is the spectral density of a deterministic process that has a very high order contact with zero due to which the Szegő condition is violated, while
g
is a nonnegative function that can have arbitrary power type singularities. We show that for spectral densities
f
from this class the prediction error
σ
n
2
(
f
)
behaves like a power as
n
→
∞
. Examples illustrate the obtained results.</description><subject>Asymptotic properties</subject><subject>Density</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Predictions</subject><subject>Stationary processes</subject><issn>0236-5294</issn><issn>1588-2632</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLwzAUx4MoOKdfwFPBczQvadrkWLvMFbZ1tp2wU6xZKw7dZrId_PamVvDm4fGHx-__HvwQugZyC4TEdw5IGIeYUIoJ0FBgeYIGwIXANGL0FA0IZRHmVIbn6MK5DSGEMxIO0HM-D5JyNVtUeZWlwb2aJE9ZXgT5OKgmKlgUapSlVeYpVRR-P_aTBOk0KcuOGalKFbNsnpVdu6ySDk2KVVCqx6Wap6q8RGdt_e6aq98couVYVekET_OHLE2m2DCQB0yF4K2hXIIJa05jKnxGrWijthEcalEbExsh61pEsI4kkVwyYHG4BqCNeWFDdNPf3dvd57FxB73ZHe3Wv9Q0hpgxwiPwFO0pY3fO2abVe_v2UdsvDUR3JnVvUnuT-seklr7E-pLz8Pa1sX-n_2l9A0c7bPQ</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>BABAYAN, N.</creator><creator>GINOVYAN, M.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220801</creationdate><title>ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES</title><author>BABAYAN, N. ; GINOVYAN, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-2885fc2591c4a52728c4a6f8f6fe851a8acc7c89aa861d69095931374d112ecb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Asymptotic properties</topic><topic>Density</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Predictions</topic><topic>Stationary processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BABAYAN, N.</creatorcontrib><creatorcontrib>GINOVYAN, M.</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BABAYAN, N.</au><au>GINOVYAN, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES</atitle><jtitle>Acta mathematica Hungarica</jtitle><stitle>Acta Math. Hungar</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>167</volume><issue>2</issue><spage>501</spage><epage>528</epage><pages>501-528</pages><issn>0236-5294</issn><eissn>1588-2632</eissn><abstract>We study the prediction problem for deterministic stationary processes
X
(
t
)
possessing spectral density
f
. We describe the asymptotic behavior of the best linear mean squared prediction error
σ
n
2
(
f
)
in predicting
X
(
0
)
given
X
(
t
)
,
-
n
≤
t
≤
-
1
, as
n
goes to infinity. We consider a class of spectral densities of the form
f
=
f
d
g
, where
f
d
is the spectral density of a deterministic process that has a very high order contact with zero due to which the Szegő condition is violated, while
g
is a nonnegative function that can have arbitrary power type singularities. We show that for spectral densities
f
from this class the prediction error
σ
n
2
(
f
)
behaves like a power as
n
→
∞
. Examples illustrate the obtained results.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10474-022-01248-9</doi><tpages>28</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0236-5294 |
ispartof | Acta mathematica Hungarica, 2022-08, Vol.167 (2), p.501-528 |
issn | 0236-5294 1588-2632 |
language | eng |
recordid | cdi_proquest_journals_2717330561 |
source | Springer Link |
subjects | Asymptotic properties Density Mathematics Mathematics and Statistics Predictions Stationary processes |
title | ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES |
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