{"id":"https://openalex.org/W7202284385","doi":"https://doi.org/10.11648/j.ajtas.20261504.13","title":"Modelling the Volatility of the USD/KES Exchange Rate Using the Nadaraya-watson Kernel Regression Estimator","display_name":"Modelling the Volatility of the USD/KES Exchange Rate Using the Nadaraya-watson Kernel Regression Estimator","publication_year":2026,"publication_date":"2026-07-28","ids":{"openalex":"https://openalex.org/W7202284385","doi":"https://doi.org/10.11648/j.ajtas.20261504.13"},"language":"en","primary_location":{"id":"doi:10.11648/j.ajtas.20261504.13","doi":"https://doi.org/10.11648/j.ajtas.20261504.13","is_oa":true,"landing_page_url":"https://doi.org/10.11648/j.ajtas.20261504.13","pdf_url":"http://article.sciencepg.com/pdf/j.ajtas.20261504.13","source":{"id":"https://openalex.org/S2764541676","display_name":"American Journal of Theoretical and Applied Statistics","issn_l":"2326-8999","issn":["2326-8999","2326-9006"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319272","host_organization_name":"Science Publishing Group","host_organization_lineage":["https://openalex.org/P4310319272"],"host_organization_lineage_names":["Science Publishing Group"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Theoretical and Applied Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://article.sciencepg.com/pdf/j.ajtas.20261504.13","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147043256","display_name":"Mary Wanjohi","orcid":"https://orcid.org/0009-0003-6592-2727","observed_orcids":["https://orcid.org/0009-0003-6592-2727"]},"institutions":[{"id":"https://openalex.org/I3131411328","display_name":"Kirinyaga University","ror":"https://ror.org/00geck193","country_code":"KE","type":"education","lineage":["https://openalex.org/I3131411328"]}],"countries":["KE"],"is_corresponding":true,"raw_author_name":"Mary Wanjohi","raw_affiliation_strings":["Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya"],"raw_orcid":"https://orcid.org/0009-0003-6592-2727","affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya","institution_ids":["https://openalex.org/I3131411328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143832055","display_name":"Josephine Ngure","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3131411328","display_name":"Kirinyaga University","ror":"https://ror.org/00geck193","country_code":"KE","type":"education","lineage":["https://openalex.org/I3131411328"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Josephine Ngure","raw_affiliation_strings":["Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya","institution_ids":["https://openalex.org/I3131411328"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058223224","display_name":"Martin M. Kithinji","orcid":"https://orcid.org/0000-0002-0449-3776","observed_orcids":["https://orcid.org/0000-0002-0449-3776"]},"institutions":[{"id":"https://openalex.org/I3131411328","display_name":"Kirinyaga University","ror":"https://ror.org/00geck193","country_code":"KE","type":"education","lineage":["https://openalex.org/I3131411328"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Martin Kithinji","raw_affiliation_strings":["Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Sciences, Kirinyaga University, Kerugoya, Kenya","institution_ids":["https://openalex.org/I3131411328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5147043256"],"corresponding_institution_ids":["https://openalex.org/I3131411328"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"4","first_page":"141","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10007","display_name":"Monetary Policy and Economic Impact","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11059","display_name":"Market Dynamics and Volatility","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exchange-rate-volatility","display_name":"exchange rate volatility","score":0.9909999966621399},{"id":"https://openalex.org/keywords/nadaraya-watson-kernel-regression","display_name":"Nadaraya-Watson kernel regression","score":0.9369999766349792},{"id":"https://openalex.org/keywords/nonparametric-volatility-estimation","display_name":"nonparametric volatility estimation","score":0.8659999966621399},{"id":"https://openalex.org/keywords/bandwidth-selection","display_name":"bandwidth selection","score":0.7900000214576721},{"id":"https://openalex.org/keywords/kenyan-shilling","display_name":"Kenyan shilling","score":0.7480000257492065},{"id":"https://openalex.org/keywords/emerging-market-currencies","display_name":"emerging market currencies","score":0.7710000276565552},{"id":"https://openalex.org/keywords/2008-financial-crisis","display_name":"2008 financial crisis","score":0.8640000224113464}],"concepts":[{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.6718000173568726},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.5760999917984009},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.5629000067710876},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.5368000268936157},{"id":"https://openalex.org/C2776988154","wikidata":"https://www.wikidata.org/wiki/Q66100","display_name":"Exchange rate","level":2,"score":0.5325000286102295},{"id":"https://openalex.org/C117996083","wikidata":"https://www.wikidata.org/wiki/Q5473296","display_name":"Forward volatility","level":4,"score":0.5088000297546387},{"id":"https://openalex.org/C24189920","wikidata":"https://www.wikidata.org/wiki/Q1660345","display_name":"Implied volatility","level":3,"score":0.49799999594688416},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46160000562667847},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.46059998869895935},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.42820000648498535},{"id":"https://openalex.org/C165603445","wikidata":"https://www.wikidata.org/wiki/Q7915766","display_name":"Variance swap","level":5,"score":0.4131999909877777},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3995000123977661},{"id":"https://openalex.org/C60092789","wikidata":"https://www.wikidata.org/wiki/Q7301291","display_name":"Realized variance","level":3,"score":0.37560001015663147},{"id":"https://openalex.org/C120488996","wikidata":"https://www.wikidata.org/wiki/Q17016064","display_name":"Variance function","level":3,"score":0.36730000376701355},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3635999858379364},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C141121606","wikidata":"https://www.wikidata.org/wiki/Q8142","display_name":"Currency","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.3160000145435333},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C13290067","wikidata":"https://www.wikidata.org/wiki/Q915788","display_name":"Volatility smile","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C89218465","wikidata":"https://www.wikidata.org/wiki/Q5449732","display_name":"Financial models with long-tailed distributions and volatility clustering","level":5,"score":0.27959999442100525},{"id":"https://openalex.org/C536366893","wikidata":"https://www.wikidata.org/wiki/Q66076","display_name":"Foreign exchange market","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C187625094","wikidata":"https://www.wikidata.org/wiki/Q7388452","display_name":"SABR volatility model","level":4,"score":0.25780001282691956},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.25429999828338623},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C44731940","wikidata":"https://www.wikidata.org/wiki/Q7940001","display_name":"Volatility risk premium","level":4,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.11648/j.ajtas.20261504.13","doi":"https://doi.org/10.11648/j.ajtas.20261504.13","is_oa":true,"landing_page_url":"https://doi.org/10.11648/j.ajtas.20261504.13","pdf_url":"http://article.sciencepg.com/pdf/j.ajtas.20261504.13","source":{"id":"https://openalex.org/S2764541676","display_name":"American Journal of Theoretical and Applied Statistics","issn_l":"2326-8999","issn":["2326-8999","2326-9006"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319272","host_organization_name":"Science Publishing Group","host_organization_lineage":["https://openalex.org/P4310319272"],"host_organization_lineage_names":["Science Publishing Group"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Theoretical and Applied Statistics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.11648/j.ajtas.20261504.13","doi":"https://doi.org/10.11648/j.ajtas.20261504.13","is_oa":true,"landing_page_url":"https://doi.org/10.11648/j.ajtas.20261504.13","pdf_url":"http://article.sciencepg.com/pdf/j.ajtas.20261504.13","source":{"id":"https://openalex.org/S2764541676","display_name":"American Journal of Theoretical and Applied Statistics","issn_l":"2326-8999","issn":["2326-8999","2326-9006"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319272","host_organization_name":"Science Publishing Group","host_organization_lineage":["https://openalex.org/P4310319272"],"host_organization_lineage_names":["Science Publishing Group"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Theoretical and Applied Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7202284385.pdf","grobid_xml":"https://content.openalex.org/works/W7202284385.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1545599178","https://openalex.org/W1971713783","https://openalex.org/W1979575715","https://openalex.org/W1999996900","https://openalex.org/W2071661189","https://openalex.org/W2101424588","https://openalex.org/W2129905273","https://openalex.org/W2164175562","https://openalex.org/W2489540272","https://openalex.org/W2569708144","https://openalex.org/W3122175640","https://openalex.org/W3126328521","https://openalex.org/W4235667863","https://openalex.org/W4401175580"],"related_works":["https://openalex.org/W2903989437","https://openalex.org/W3201529782","https://openalex.org/W3188995337","https://openalex.org/W2140721136","https://openalex.org/W4417194444","https://openalex.org/W4321380506","https://openalex.org/W4293240866","https://openalex.org/W2599011948","https://openalex.org/W2565635230","https://openalex.org/W2404516603"],"abstract_inverted_index":{"Exchange":[0],"rate":[1,34],"volatility":[2,24,84,134,149,172,201],"poses":[3],"significant":[4],"challenges":[5],"for":[6,112,119,168,211],"economic":[7],"planning,":[8],"risk":[9],"management,":[10],"and":[11,72,95,118,183],"policy":[12],"formulation":[13],"in":[14,82],"emerging":[15,212],"economies":[16],"such":[17],"as":[18],"Kenya.":[19],"This":[20],"study":[21,190],"models":[22,89],"the":[23,26,36,46,67,83,113,120,133,175,179,184,193,216],"of":[25,49,129,166],"United":[27],"States":[28],"Dollar/":[29],"Kenyan":[30,217],"Shillings":[31],"(USD/KES)":[32],"exchange":[33],"using":[35,69,101],"nonparametric":[37],"Nadaraya-Watson":[38,64,194],"kernel":[39,70,104,195],"regression":[40,196],"estimator.":[41],"Daily":[42],"buying":[43],"rates":[44],"from":[45],"Central":[47],"Bank":[48],"Kenya":[50],"spanning":[51],"January":[52],"2,":[53],"2003,":[54],"to":[55,77,79],"December":[56],"29,":[57],"2023":[58],"(4,764":[59],"observations)":[60],"were":[61,99],"used.":[62],"The":[63,92,109,139,157,189],"estimator":[65,197],"smooths":[66],"data":[68],"functions":[71,98],"bandwidth":[73,111,127],"parameters,":[74],"enabling":[75],"it":[76,209],"adapt":[78],"localized":[80],"features":[81],"pattern":[85],"that":[86,132,192],"conventional":[87],"parametric":[88,206],"may":[90],"overlook.":[91],"conditional":[93,96,114,121,140],"mean":[94,115],"variance":[97,122,141],"estimated":[100],"a":[102,126,144,160],"Gaussian":[103],"with":[105,125],"cross-validated":[106],"fixed":[107],"bandwidths.":[108],"optimal":[110],"was":[116,123],"0.02750928":[117],"0.1349632,":[124],"ratio":[128],"4.905869,":[130],"indicating":[131],"function":[135,142],"requires":[136],"smoother":[137],"estimation.":[138],"exhibited":[143],"distinct":[145],"U-shape,":[146],"showing":[147],"higher":[148],"following":[150],"extreme":[151],"positive":[152],"or":[153],"negative":[154],"lagged":[155],"returns.":[156],"model":[158],"achieved":[159],"Root":[161],"Mean":[162],"Squared":[163],"Error":[164],"(RMSE)":[165],"1.919":[167],"variance,":[169],"capturing":[170],"major":[171],"episodes":[173],"including":[174],"2008-2009":[176],"financial":[177],"crisis,":[178,182],"2011":[180],"currency":[181],"2016":[185],"reserves":[186],"depletion":[187],"shock.":[188],"concludes":[191],"successfully":[198],"captures":[199],"nonlinear":[200],"dynamics":[202],"without":[203],"imposing":[204],"rigid":[205],"assumptions,":[207],"making":[208],"suitable":[210],"market":[213],"currencies":[214],"like":[215],"shilling.":[218]},"counts_by_year":[],"updated_date":"2026-09-25T08:18:29.962427","created_date":"2026-08-13T00:00:00"}