{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T17:42:58Z","timestamp":1763142178668,"version":"3.40.5"},"reference-count":17,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude.\nThe periodicity of the frequency components is also thought to affect the convergence of these parameters.\nIn this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal.\nUnder the high-frequency sampling setting, we provide the frequency components\u2019 consistency and asymptotic normality.\nIt is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein\u2013Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein\u2013Uhlenbeck process, <jats:italic>Monte Carlo Methods Appl.<\/jats:italic>\n                  <jats:bold>29<\/jats:bold> (2023), 1, 1\u201332].\nThe result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic.\nIn this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components.\nFurther, the result of the study, that is, the convergence rate of the frequency is <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msqrt>\n                              <m:msup>\n                                 <m:mrow>\n                                    <m:mo stretchy=\"false\">(<\/m:mo>\n                                    <m:mrow>\n                                       <m:mi>n<\/m:mi>\n                                       <m:mo>\u2062<\/m:mo>\n                                       <m:mi>h<\/m:mi>\n                                    <\/m:mrow>\n                                    <m:mo stretchy=\"false\">)<\/m:mo>\n                                 <\/m:mrow>\n                                 <m:mn>3<\/m:mn>\n                              <\/m:msup>\n                           <\/m:msqrt>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2023-2020_ineq_0001.png\"\/>\n                        <jats:tex-math>\\sqrt{(nh)^{3}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, <jats:italic>J. Math. Comput. Sci.<\/jats:italic>\n                  <jats:bold>11<\/jats:bold> (2021), 5, 6433\u20136443], which mentioned <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msqrt>\n                              <m:mrow>\n                                 <m:msup>\n                                    <m:mrow>\n                                       <m:mo stretchy=\"false\">(<\/m:mo>\n                                       <m:mrow>\n                                          <m:mi>n<\/m:mi>\n                                          <m:mo>\u2062<\/m:mo>\n                                          <m:mi>h<\/m:mi>\n                                       <\/m:mrow>\n                                       <m:mo stretchy=\"false\">)<\/m:mo>\n                                    <\/m:mrow>\n                                    <m:mn>3<\/m:mn>\n                                 <\/m:msup>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi>h<\/m:mi>\n                              <\/m:mrow>\n                           <\/m:msqrt>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2023-2020_ineq_0002.png\"\/>\n                        <jats:tex-math>\\sqrt{(nh)^{3}h}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nThe proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.<\/jats:p>","DOI":"10.1515\/mcma-2023-2020","type":"journal-article","created":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T17:57:58Z","timestamp":1699639078000},"page":"43-53","source":"Crossref","is-referenced-by-count":1,"title":["On the estimation of periodic signals in the diffusion process using a high-frequency scheme"],"prefix":"10.1515","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9964-6693","authenticated-orcid":false,"given":"Getut","family":"Pramesti","sequence":"first","affiliation":[{"name":"Mathematics Education Department , Universitas Sebelas Maret , Jl. Ir. Sutami 36A , Surakarta 57126 , Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8435-3230","authenticated-orcid":false,"given":"Ristu","family":"Saptono","sequence":"additional","affiliation":[{"name":"Informatics Department , Universitas Sebelas Maret , Jl. Ir. Sutami 36A , Surakarta 57126 , Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,11,11]]},"reference":[{"key":"2024022618254296424_j_mcma-2023-2020_ref_001","doi-asserted-by":"crossref","unstructured":"O. Besson and P. Stoica,\nNonlinear least-squares approach to frequency estimation and detection for sinusoidal signals with arbitrary envelope,\nDigital Signal Process. 9 (1999), no. 1, 45\u201356.","DOI":"10.1006\/dspr.1998.0330"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_002","unstructured":"J. Brownlee,\nMachine Learning Mastery with Python: Understand your Data, Create Accurate Models, and work Projects End-to-End,\nMachine Learning Mastery, 2016."},{"key":"2024022618254296424_j_mcma-2023-2020_ref_003","doi-asserted-by":"crossref","unstructured":"L. M. Candanedo, V. Feldheim and D. Deramaix,\nData driven prediction models of energy use of appliances in a low-energy house,\nEnergy Buildings 140 (2017), 81\u201397.","DOI":"10.1016\/j.enbuild.2017.01.083"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_004","unstructured":"V. Genon-Catalot and J. Jacod,\nOn the estimation of the diffusion coefficient for multi-dimensional diffusion processes,\nAnn. Inst. H. Poincar\u00e9 Probab. Statist. 29 (1993), no. 1, 119\u2013151."},{"key":"2024022618254296424_j_mcma-2023-2020_ref_005","doi-asserted-by":"crossref","unstructured":"S. M. Iacus,\nSimulation and Inference for Stochastic Differential Equations,\nSpringer Ser. Statist.,\nSpringer, New York, 2009.","DOI":"10.1007\/978-0-387-75839-8"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_006","doi-asserted-by":"crossref","unstructured":"I. A. Ibragimov and R. Z. Has\u2019minskii,\nSeveral estimation problems in a Gaussian white noise,\nStatistical Estimation,\nSpringer, New York (1981), 321\u2013361.","DOI":"10.1007\/978-1-4899-0027-2_9"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_007","doi-asserted-by":"crossref","unstructured":"L. Igual and S. Segu\u00ed,\nIntroduction to Data Science,\nUndergrad. Top. Comput. Sci,\nSpringer, Cham, 2017.","DOI":"10.1007\/978-3-319-50017-1"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_008","doi-asserted-by":"crossref","unstructured":"D. Kundu,\nAsymptotic theory of least squares estimator of a particular nonlinear regression model,\nStatist. Probab. Lett. 18 (1993), no. 1, 13\u201317.","DOI":"10.1016\/0167-7152(93)90093-X"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_009","unstructured":"S. Nandi and D. Kundu,\nStatistical Signal Processing\u2014Frequency Estimation,\nSpringer,Singapore, 2012."},{"key":"2024022618254296424_j_mcma-2023-2020_ref_010","unstructured":"B. \u00d8ksendal,\nStochastic Differential Equations: An Introduction with Applications,\nUniversitext,\nSpringer, Berlin, 2013."},{"key":"2024022618254296424_j_mcma-2023-2020_ref_011","unstructured":"G. Pramesti,\nThe least-squares estimator of sinusoidal signal of diffusion process for discrete observations,\nJ. Math. Comput. Sci. 11 (2021), no. 5, 6433\u20136443."},{"key":"2024022618254296424_j_mcma-2023-2020_ref_012","doi-asserted-by":"crossref","unstructured":"G. Pramesti,\nParameter least-squares estimation for time-inhomogeneous Ornstein\u2013Uhlenbeck process,\nMonte Carlo Methods Appl. 29 (2023), no. 1, 1\u201332.","DOI":"10.1515\/mcma-2022-2127"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_013","doi-asserted-by":"crossref","unstructured":"P. Stoica, T. S\u00f6derstr\u00f6m and F. N. Ti,\nAsymptotic properties of the high-order Yule\u2013Walker estimates of sinusoidal frequencies,\nIEEE Trans. Acoust. Speech Signal Process. 37 (1989), no. 11, 1721\u20131734.","DOI":"10.1109\/29.46554"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_014","doi-asserted-by":"crossref","unstructured":"A. M. Walker,\nOn the estimation of a harmonic component in a time series with stationary independent residuals,\nBiometrika 58 (1971), 21\u201336.","DOI":"10.1093\/biomet\/58.1.21"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_015","doi-asserted-by":"crossref","unstructured":"P. Whittle,\nThe simultaneous estimation of a time series harmonic components and covariance structure,\nTrabajos Estad\u00edst. 3 (1952), 43\u201357.","DOI":"10.1007\/BF03002861"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_016","doi-asserted-by":"crossref","unstructured":"I. Ziskind and M. Wax,\nMaximum likelihood localization of multiple sources by alternating projection,\nIEEE Trans Acoust. Speech Signal Process. 36 (1988), no. 10, 1553\u20131560.","DOI":"10.1109\/29.7543"},{"key":"2024022618254296424_j_mcma-2023-2020_ref_017","unstructured":"UCI Machine Learning Repository, Belgium household energy prediction."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2020\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2020\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T18:26:20Z","timestamp":1708971980000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2020\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,11]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,3,1]]},"published-print":{"date-parts":[[2024,3,1]]}},"alternative-id":["10.1515\/mcma-2023-2020"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2023-2020","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2023,11,11]]}}}