Testing for parameter change epochs in GARCH time series Article Swipe
Stefan Richter
,
Ning Wang
,
Wei Biao Wu
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1093/ectj/utad006
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1093/ectj/utad006
Summary We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against the alternative that there is an ‘abnormal’ period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process. Simulations in the Appendix show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e., the Bitcoin returns.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1093/ectj/utad006
- https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdf
- OA Status
- hybrid
- Cited By
- 6
- References
- 29
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4318756745
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4318756745Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1093/ectj/utad006Digital Object Identifier
- Title
-
Testing for parameter change epochs in GARCH time seriesWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-02-01Full publication date if available
- Authors
-
Stefan Richter, Ning Wang, Wei Biao WuList of authors in order
- Landing page
-
https://doi.org/10.1093/ectj/utad006Publisher landing page
- PDF URL
-
https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdfDirect OA link when available
- Concepts
-
Autoregressive conditional heteroskedasticity, Heteroscedasticity, Volatility (finance), Econometrics, Autoregressive model, Mathematics, Test statistic, Series (stratigraphy), Statistics, Statistical hypothesis testing, Applied mathematics, Biology, PaleontologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 3, 2024: 3Per-year citation counts (last 5 years)
- References (count)
-
29Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4318756745 |
|---|---|
| doi | https://doi.org/10.1093/ectj/utad006 |
| ids.doi | https://doi.org/10.1093/ectj/utad006 |
| ids.openalex | https://openalex.org/W4318756745 |
| fwci | 3.69092801 |
| type | article |
| title | Testing for parameter change epochs in GARCH time series |
| awards[0].id | https://openalex.org/G4720358549 |
| awards[0].funder_id | https://openalex.org/F4320334630 |
| awards[0].display_name | |
| awards[0].funder_award_id | ES/T01573X/1 |
| awards[0].funder_display_name | Economic and Social Research Council |
| biblio.issue | 3 |
| biblio.volume | 26 |
| biblio.last_page | 491 |
| biblio.first_page | 467 |
| topics[0].id | https://openalex.org/T11059 |
| topics[0].field.id | https://openalex.org/fields/20 |
| topics[0].field.display_name | Economics, Econometrics and Finance |
| topics[0].score | 0.9990000128746033 |
| topics[0].domain.id | https://openalex.org/domains/2 |
| topics[0].domain.display_name | Social Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2002 |
| topics[0].subfield.display_name | Economics and Econometrics |
| topics[0].display_name | Market Dynamics and Volatility |
| topics[1].id | https://openalex.org/T10282 |
| topics[1].field.id | https://openalex.org/fields/20 |
| topics[1].field.display_name | Economics, Econometrics and Finance |
| topics[1].score | 0.9988999962806702 |
| topics[1].domain.id | https://openalex.org/domains/2 |
| topics[1].domain.display_name | Social Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2003 |
| topics[1].subfield.display_name | Finance |
| topics[1].display_name | Financial Risk and Volatility Modeling |
| topics[2].id | https://openalex.org/T11270 |
| topics[2].field.id | https://openalex.org/fields/20 |
| topics[2].field.display_name | Economics, Econometrics and Finance |
| topics[2].score | 0.9988999962806702 |
| topics[2].domain.id | https://openalex.org/domains/2 |
| topics[2].domain.display_name | Social Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2002 |
| topics[2].subfield.display_name | Economics and Econometrics |
| topics[2].display_name | Complex Systems and Time Series Analysis |
| funders[0].id | https://openalex.org/F4320334630 |
| funders[0].ror | https://ror.org/03n0ht308 |
| funders[0].display_name | Economic and Social Research Council |
| is_xpac | False |
| apc_list.value | 3099 |
| apc_list.currency | GBP |
| apc_list.value_usd | 3801 |
| apc_paid.value | 3099 |
| apc_paid.currency | GBP |
| apc_paid.value_usd | 3801 |
| concepts[0].id | https://openalex.org/C23922673 |
| concepts[0].level | 3 |
| concepts[0].score | 0.8706227540969849 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q180752 |
| concepts[0].display_name | Autoregressive conditional heteroskedasticity |
| concepts[1].id | https://openalex.org/C101104100 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6843076944351196 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q1063540 |
| concepts[1].display_name | Heteroscedasticity |
| concepts[2].id | https://openalex.org/C91602232 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6612043380737305 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q756115 |
| concepts[2].display_name | Volatility (finance) |
| concepts[3].id | https://openalex.org/C149782125 |
| concepts[3].level | 1 |
| concepts[3].score | 0.6557847857475281 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q160039 |
| concepts[3].display_name | Econometrics |
| concepts[4].id | https://openalex.org/C159877910 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5688780546188354 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q2202883 |
| concepts[4].display_name | Autoregressive model |
| concepts[5].id | https://openalex.org/C33923547 |
| concepts[5].level | 0 |
| concepts[5].score | 0.5441293716430664 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[5].display_name | Mathematics |
| concepts[6].id | https://openalex.org/C169857963 |
| concepts[6].level | 3 |
| concepts[6].score | 0.5413830280303955 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q1461038 |
| concepts[6].display_name | Test statistic |
| concepts[7].id | https://openalex.org/C143724316 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4899265170097351 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q312468 |
| concepts[7].display_name | Series (stratigraphy) |
| concepts[8].id | https://openalex.org/C105795698 |
| concepts[8].level | 1 |
| concepts[8].score | 0.39368343353271484 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[8].display_name | Statistics |
| concepts[9].id | https://openalex.org/C87007009 |
| concepts[9].level | 2 |
| concepts[9].score | 0.3572017550468445 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q210832 |
| concepts[9].display_name | Statistical hypothesis testing |
| concepts[10].id | https://openalex.org/C28826006 |
| concepts[10].level | 1 |
| concepts[10].score | 0.3528887927532196 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[10].display_name | Applied mathematics |
| concepts[11].id | https://openalex.org/C86803240 |
| concepts[11].level | 0 |
| concepts[11].score | 0.0 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[11].display_name | Biology |
| concepts[12].id | https://openalex.org/C151730666 |
| concepts[12].level | 1 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q7205 |
| concepts[12].display_name | Paleontology |
| keywords[0].id | https://openalex.org/keywords/autoregressive-conditional-heteroskedasticity |
| keywords[0].score | 0.8706227540969849 |
| keywords[0].display_name | Autoregressive conditional heteroskedasticity |
| keywords[1].id | https://openalex.org/keywords/heteroscedasticity |
| keywords[1].score | 0.6843076944351196 |
| keywords[1].display_name | Heteroscedasticity |
| keywords[2].id | https://openalex.org/keywords/volatility |
| keywords[2].score | 0.6612043380737305 |
| keywords[2].display_name | Volatility (finance) |
| keywords[3].id | https://openalex.org/keywords/econometrics |
| keywords[3].score | 0.6557847857475281 |
| keywords[3].display_name | Econometrics |
| keywords[4].id | https://openalex.org/keywords/autoregressive-model |
| keywords[4].score | 0.5688780546188354 |
| keywords[4].display_name | Autoregressive model |
| keywords[5].id | https://openalex.org/keywords/mathematics |
| keywords[5].score | 0.5441293716430664 |
| keywords[5].display_name | Mathematics |
| keywords[6].id | https://openalex.org/keywords/test-statistic |
| keywords[6].score | 0.5413830280303955 |
| keywords[6].display_name | Test statistic |
| keywords[7].id | https://openalex.org/keywords/series |
| keywords[7].score | 0.4899265170097351 |
| keywords[7].display_name | Series (stratigraphy) |
| keywords[8].id | https://openalex.org/keywords/statistics |
| keywords[8].score | 0.39368343353271484 |
| keywords[8].display_name | Statistics |
| keywords[9].id | https://openalex.org/keywords/statistical-hypothesis-testing |
| keywords[9].score | 0.3572017550468445 |
| keywords[9].display_name | Statistical hypothesis testing |
| keywords[10].id | https://openalex.org/keywords/applied-mathematics |
| keywords[10].score | 0.3528887927532196 |
| keywords[10].display_name | Applied mathematics |
| language | en |
| locations[0].id | doi:10.1093/ectj/utad006 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S33519306 |
| locations[0].source.issn | 1368-4221, 1368-423X |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 1368-4221 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Econometrics Journal |
| locations[0].source.host_organization | https://openalex.org/P4310311648 |
| locations[0].source.host_organization_name | Oxford University Press |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310311648, https://openalex.org/P4310311647 |
| locations[0].source.host_organization_lineage_names | Oxford University Press, University of Oxford |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | The Econometrics Journal |
| locations[0].landing_page_url | https://doi.org/10.1093/ectj/utad006 |
| locations[1].id | pmh:oai:uchicago.tind.io:5935 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306402460 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | Knowledge@UChicago (University of Chicago) |
| locations[1].source.host_organization | https://openalex.org/I40347166 |
| locations[1].source.host_organization_name | University of Chicago |
| locations[1].source.host_organization_lineage | https://openalex.org/I40347166 |
| locations[1].license | cc-by-nc-nd |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | Text |
| locations[1].license_id | https://openalex.org/licenses/cc-by-nc-nd |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | http://knowledge.uchicago.edu/record/5935 |
| locations[1].landing_page_url | http://knowledge.uchicago.edu/record/5935 |
| locations[2].id | pmh:oai:RePEc:oup:emjrnl:v:26:y:2023:i:3:p:467-491. |
| locations[2].is_oa | False |
| locations[2].source.id | https://openalex.org/S4306401271 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | RePEc: Research Papers in Economics |
| locations[2].source.host_organization | https://openalex.org/I77793887 |
| locations[2].source.host_organization_name | Federal Reserve Bank of St. Louis |
| locations[2].source.host_organization_lineage | https://openalex.org/I77793887 |
| locations[2].license | |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | article |
| locations[2].license_id | |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | http://hdl.handle.net/10.1093/ectj/utad006 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5055274857 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-5373-8381 |
| authorships[0].author.display_name | Stefan Richter |
| authorships[0].countries | DE |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I223822909 |
| authorships[0].affiliations[0].raw_affiliation_string | Heidelberg University, Institute of Applied Mathematics , Im Neuenheimer Feld 205, 69120 Heidelberg, Germany |
| authorships[0].institutions[0].id | https://openalex.org/I223822909 |
| authorships[0].institutions[0].ror | https://ror.org/038t36y30 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I223822909 |
| authorships[0].institutions[0].country_code | DE |
| authorships[0].institutions[0].display_name | Heidelberg University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Stefan Richter |
| authorships[0].is_corresponding | True |
| authorships[0].raw_affiliation_strings | Heidelberg University, Institute of Applied Mathematics , Im Neuenheimer Feld 205, 69120 Heidelberg, Germany |
| authorships[1].author.id | https://openalex.org/A5058107332 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-1745-1425 |
| authorships[1].author.display_name | Ning Wang |
| authorships[1].countries | GB |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I52099693 |
| authorships[1].affiliations[0].raw_affiliation_string | University of York , York YO10 5DD, UK |
| authorships[1].institutions[0].id | https://openalex.org/I52099693 |
| authorships[1].institutions[0].ror | https://ror.org/04m01e293 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I52099693 |
| authorships[1].institutions[0].country_code | GB |
| authorships[1].institutions[0].display_name | University of York |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Weining Wang |
| authorships[1].is_corresponding | True |
| authorships[1].raw_affiliation_strings | University of York , York YO10 5DD, UK |
| authorships[2].author.id | https://openalex.org/A5036683934 |
| authorships[2].author.orcid | https://orcid.org/0000-0003-4310-9965 |
| authorships[2].author.display_name | Wei Biao Wu |
| authorships[2].countries | US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I40347166 |
| authorships[2].affiliations[0].raw_affiliation_string | Professor, Department of Statistics and the College, University of Chicago , USA |
| authorships[2].institutions[0].id | https://openalex.org/I40347166 |
| authorships[2].institutions[0].ror | https://ror.org/024mw5h28 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I40347166 |
| authorships[2].institutions[0].country_code | US |
| authorships[2].institutions[0].display_name | University of Chicago |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Wei Biao Wu |
| authorships[2].is_corresponding | True |
| authorships[2].raw_affiliation_strings | Professor, Department of Statistics and the College, University of Chicago , USA |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdf |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Testing for parameter change epochs in GARCH time series |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11059 |
| primary_topic.field.id | https://openalex.org/fields/20 |
| primary_topic.field.display_name | Economics, Econometrics and Finance |
| primary_topic.score | 0.9990000128746033 |
| primary_topic.domain.id | https://openalex.org/domains/2 |
| primary_topic.domain.display_name | Social Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2002 |
| primary_topic.subfield.display_name | Economics and Econometrics |
| primary_topic.display_name | Market Dynamics and Volatility |
| related_works | https://openalex.org/W1608601224, https://openalex.org/W2017138702, https://openalex.org/W1978494725, https://openalex.org/W2776656900, https://openalex.org/W1968843728, https://openalex.org/W2031589205, https://openalex.org/W3029813487, https://openalex.org/W2758076833, https://openalex.org/W2523151162, https://openalex.org/W3015822731 |
| cited_by_count | 6 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 3 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 3 |
| locations_count | 3 |
| best_oa_location.id | doi:10.1093/ectj/utad006 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S33519306 |
| best_oa_location.source.issn | 1368-4221, 1368-423X |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 1368-4221 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Econometrics Journal |
| best_oa_location.source.host_organization | https://openalex.org/P4310311648 |
| best_oa_location.source.host_organization_name | Oxford University Press |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310311648, https://openalex.org/P4310311647 |
| best_oa_location.source.host_organization_lineage_names | Oxford University Press, University of Oxford |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | The Econometrics Journal |
| best_oa_location.landing_page_url | https://doi.org/10.1093/ectj/utad006 |
| primary_location.id | doi:10.1093/ectj/utad006 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S33519306 |
| primary_location.source.issn | 1368-4221, 1368-423X |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1368-4221 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Econometrics Journal |
| primary_location.source.host_organization | https://openalex.org/P4310311648 |
| primary_location.source.host_organization_name | Oxford University Press |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310311648, https://openalex.org/P4310311647 |
| primary_location.source.host_organization_lineage_names | Oxford University Press, University of Oxford |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://academic.oup.com/ectj/advance-article-pdf/doi/10.1093/ectj/utad006/49529042/utad006.pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | The Econometrics Journal |
| primary_location.landing_page_url | https://doi.org/10.1093/ectj/utad006 |
| publication_date | 2023-02-01 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2904240262, https://openalex.org/W2110769522, https://openalex.org/W3124306942, https://openalex.org/W2054477007, https://openalex.org/W1986788466, https://openalex.org/W2078935796, https://openalex.org/W2163757898, https://openalex.org/W2143975431, https://openalex.org/W1979575715, https://openalex.org/W2074416088, https://openalex.org/W1994411832, https://openalex.org/W1877414726, https://openalex.org/W2158998391, https://openalex.org/W3106947108, https://openalex.org/W6754978032, https://openalex.org/W2896420624, https://openalex.org/W2057884190, https://openalex.org/W2130974386, https://openalex.org/W1980002957, https://openalex.org/W4236290419, https://openalex.org/W1980541697, https://openalex.org/W2077115352, https://openalex.org/W1991968032, https://openalex.org/W2139238934, https://openalex.org/W2122524893, https://openalex.org/W2963629083, https://openalex.org/W1460189015, https://openalex.org/W2903504005, https://openalex.org/W2896025957 |
| referenced_works_count | 29 |
| abstract_inverted_index.a | 3, 17, 33, 90, 154, 176, 212 |
| abstract_inverted_index.It | 73 |
| abstract_inverted_index.We | 1, 88, 197 |
| abstract_inverted_index.an | 47, 63, 101 |
| abstract_inverted_index.be | 139 |
| abstract_inverted_index.in | 133, 180 |
| abstract_inverted_index.is | 46, 74 |
| abstract_inverted_index.of | 16, 32, 69, 83, 96, 107, 120, 148, 168, 175, 206, 214 |
| abstract_inverted_index.on | 117 |
| abstract_inverted_index.or | 12, 65 |
| abstract_inverted_index.to | 62, 103, 138, 141, 165, 172, 201 |
| abstract_inverted_index.we | 27 |
| abstract_inverted_index.Our | 109 |
| abstract_inverted_index.The | 150 |
| abstract_inverted_index.all | 145 |
| abstract_inverted_index.and | 8, 80, 98, 190, 211 |
| abstract_inverted_index.are | 86 |
| abstract_inverted_index.for | 6, 93, 128, 159, 192 |
| abstract_inverted_index.has | 187 |
| abstract_inverted_index.key | 151 |
| abstract_inverted_index.may | 60 |
| abstract_inverted_index.the | 10, 29, 42, 57, 70, 78, 81, 84, 94, 105, 118, 121, 125, 129, 134, 160, 169, 173, 181, 185, 199, 202, 208, 215, 220 |
| abstract_inverted_index.both | 77, 207 |
| abstract_inverted_index.good | 188 |
| abstract_inverted_index.hold | 112, 142 |
| abstract_inverted_index.lead | 61 |
| abstract_inverted_index.long | 194 |
| abstract_inverted_index.mild | 114 |
| abstract_inverted_index.need | 137 |
| abstract_inverted_index.null | 30 |
| abstract_inverted_index.over | 144 |
| abstract_inverted_index.show | 183 |
| abstract_inverted_index.size | 189 |
| abstract_inverted_index.test | 5, 28, 92, 170, 186, 200 |
| abstract_inverted_index.that | 44, 76, 184 |
| abstract_inverted_index.then | 99 |
| abstract_inverted_index.this | 55 |
| abstract_inverted_index.time | 195 |
| abstract_inverted_index.weak | 156, 166 |
| abstract_inverted_index.with | 38, 50 |
| abstract_inverted_index.GARCH | 36, 122, 135 |
| abstract_inverted_index.apply | 198 |
| abstract_inverted_index.i.e., | 219 |
| abstract_inverted_index.leads | 164 |
| abstract_inverted_index.model | 136 |
| abstract_inverted_index.power | 191 |
| abstract_inverted_index.there | 45 |
| abstract_inverted_index.under | 113 |
| abstract_inverted_index.which | 163 |
| abstract_inverted_index.During | 54 |
| abstract_inverted_index.breaks | 85 |
| abstract_inverted_index.change | 59 |
| abstract_inverted_index.dating | 9 |
| abstract_inverted_index.market | 210 |
| abstract_inverted_index.mildly | 13, 66 |
| abstract_inverted_index.moment | 115 |
| abstract_inverted_index.period | 49 |
| abstract_inverted_index.stable | 35 |
| abstract_inverted_index.timing | 82 |
| abstract_inverted_index.(GARCH) | 24 |
| abstract_inverted_index.Bahadur | 157 |
| abstract_inverted_index.Bitcoin | 221 |
| abstract_inverted_index.Fintech | 217 |
| abstract_inverted_index.Namely, | 26 |
| abstract_inverted_index.Summary | 0 |
| abstract_inverted_index.against | 41 |
| abstract_inverted_index.assumed | 75 |
| abstract_inverted_index.breaks, | 97 |
| abstract_inverted_index.change. | 149 |
| abstract_inverted_index.changed | 51 |
| abstract_inverted_index.develop | 2, 89 |
| abstract_inverted_index.involve | 153 |
| abstract_inverted_index.market, | 218 |
| abstract_inverted_index.period, | 56 |
| abstract_inverted_index.periods | 106, 147 |
| abstract_inverted_index.process | 37 |
| abstract_inverted_index.provide | 100 |
| abstract_inverted_index.results | 111, 152 |
| abstract_inverted_index.series. | 196 |
| abstract_inverted_index.supreme | 174 |
| abstract_inverted_index.uniform | 4, 155 |
| abstract_inverted_index.values. | 53 |
| abstract_inverted_index.Appendix | 182 |
| abstract_inverted_index.Gaussian | 177 |
| abstract_inverted_index.changes. | 108 |
| abstract_inverted_index.constant | 39 |
| abstract_inverted_index.emerging | 216 |
| abstract_inverted_index.existing | 126 |
| abstract_inverted_index.globally | 34 |
| abstract_inverted_index.identify | 104 |
| abstract_inverted_index.possible | 146 |
| abstract_inverted_index.process. | 25, 72, 123, 178 |
| abstract_inverted_index.returns. | 222 |
| abstract_inverted_index.strictly | 18 |
| abstract_inverted_index.unknown. | 87 |
| abstract_inverted_index.algorithm | 102 |
| abstract_inverted_index.behaviour | 15, 68 |
| abstract_inverted_index.detecting | 7 |
| abstract_inverted_index.estimated | 161 |
| abstract_inverted_index.existence | 95 |
| abstract_inverted_index.explosive | 14, 67 |
| abstract_inverted_index.financial | 209 |
| abstract_inverted_index.magnitude | 79 |
| abstract_inverted_index.parameter | 52 |
| abstract_inverted_index.statistic | 171 |
| abstract_inverted_index.uniformly | 143 |
| abstract_inverted_index.estimation | 132 |
| abstract_inverted_index.hypothesis | 31 |
| abstract_inverted_index.indicators | 205 |
| abstract_inverted_index.integrated | 11, 64 |
| abstract_inverted_index.likelihood | 131 |
| abstract_inverted_index.parameters | 40 |
| abstract_inverted_index.properties | 127 |
| abstract_inverted_index.reasonably | 193 |
| abstract_inverted_index.stationary | 19 |
| abstract_inverted_index.volatility | 71 |
| abstract_inverted_index.Simulations | 179 |
| abstract_inverted_index.alternative | 43 |
| abstract_inverted_index.assumptions | 116 |
| abstract_inverted_index.conditional | 22 |
| abstract_inverted_index.convergence | 167 |
| abstract_inverted_index.generalized | 20 |
| abstract_inverted_index.innovations | 119 |
| abstract_inverted_index.parameters, | 162 |
| abstract_inverted_index.theoretical | 110 |
| abstract_inverted_index.Technically, | 124 |
| abstract_inverted_index.conventional | 203 |
| abstract_inverted_index.early-warning | 204 |
| abstract_inverted_index.quasi-maximum | 130 |
| abstract_inverted_index.autoregressive | 21 |
| abstract_inverted_index.double-supreme | 91 |
| abstract_inverted_index.reinvestigated | 140 |
| abstract_inverted_index.representation | 158 |
| abstract_inverted_index.representative | 213 |
| abstract_inverted_index.‘abnormal’ | 48 |
| abstract_inverted_index.parameter-value | 58 |
| abstract_inverted_index.heteroskedasticity | 23 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 96 |
| corresponding_author_ids | https://openalex.org/A5058107332, https://openalex.org/A5036683934, https://openalex.org/A5055274857 |
| countries_distinct_count | 3 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I223822909, https://openalex.org/I40347166, https://openalex.org/I52099693 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.4000000059604645 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile.value | 0.9232887 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |