In many applications involving data collected over time, it is important to get timely estimates and adjustments of the parameters associated with a dynamic model. When the dynamics of the model must be updated, time and computational simplicity are important issues. When the dynamic system is not linear the problem of adaptation and response to feedback are exacerbated. A linear approximation of the process at various levels or “states” may approximate the non-linear system. In this case the approximation is linear within a state and transitions from state to state over time. The transition probabilities are parametrized as a Markov chain, and the within-state dynamics are modeled by an AR time series model. However, in order to make the estimates available almost instantaneously, least squares and weighted least squares estimates are used. This is a modification of the cluster-weighted models proposed by Gershenfeld, Schoner, and Metois (1999). A simulation study compares the models and explores the adequacy of least squares estimators.
","abstract_html":"<p>In many applications involving data collected over time, it is important to get timely estimates and adjustments of the parameters associated with a dynamic model. When the dynamics of the model must be updated, time and computational simplicity are important issues. When the dynamic system is not linear the problem of adaptation and response to feedback are exacerbated. A linear approximation of the process at various levels or “states” may approximate the non-linear system. In this case the approximation is linear within a state and transitions from state to state over time. The transition probabilities are parametrized as a Markov chain, and the within-state dynamics are modeled by an AR time series model. However, in order to make the estimates available almost instantaneously, least squares and weighted least squares estimates are used. This is a modification of the cluster-weighted models proposed by Gershenfeld, Schoner, and Metois (1999). A simulation study compares the models and explores the adequacy of least squares estimators.</p>","abstract_has_math":false,"creators":["Lyman, Mark Ballatore"],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:54Z","subjects":["cluster-weighted","nonlinear","time series","Statistics and Probability"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/1170","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Lyman, Mark Ballatore"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-07-11T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["cluster-weighted","nonlinear","time series","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/1170","https://scholarsarchive.byu.edu/context/etd/article/2169/viewcontent/ETD_CISOPTR_1174.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Statistics"]},{"key":"dc:description.abstract","label":"Abstract","values":["In many applications involving data collected over time, it is important to get timely estimates and adjustments of the parameters associated with a dynamic model. When the dynamics of the model must be updated, time and computational simplicity are important issues. When the dynamic system is not linear the problem of adaptation and response to feedback are exacerbated. A linear approximation of the process at various levels or “states” may approximate the non-linear system. In this case the approximation is linear within a state and transitions from state to state over time. The transition probabilities are parametrized as a Markov chain, and the within-state dynamics are modeled by an AR time series model. However, in order to make the estimates available almost instantaneously, least squares and weighted least squares estimates are used. This is a modification of the cluster-weighted models proposed by Gershenfeld, Schoner, and Metois (1999). A simulation study compares the models and explores the adequacy of least squares estimators.
"]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["A Modified Cluster-Weighted Approach to Nonlinear Time Series"]}]}],"canonical_facts":{"dc:creator":["Lyman, Mark Ballatore"],"dc:date":["2007-07-11T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Statistics"],"dc:description.abstract":["In many applications involving data collected over time, it is important to get timely estimates and adjustments of the parameters associated with a dynamic model. When the dynamics of the model must be updated, time and computational simplicity are important issues. When the dynamic system is not linear the problem of adaptation and response to feedback are exacerbated. A linear approximation of the process at various levels or “states” may approximate the non-linear system. In this case the approximation is linear within a state and transitions from state to state over time. The transition probabilities are parametrized as a Markov chain, and the within-state dynamics are modeled by an AR time series model. However, in order to make the estimates available almost instantaneously, least squares and weighted least squares estimates are used. This is a modification of the cluster-weighted models proposed by Gershenfeld, Schoner, and Metois (1999). A simulation study compares the models and explores the adequacy of least squares estimators.
"],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/1170","https://scholarsarchive.byu.edu/context/etd/article/2169/viewcontent/ETD_CISOPTR_1174.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["cluster-weighted","nonlinear","time series","Statistics and Probability"],"dc:title":["A Modified Cluster-Weighted Approach to Nonlinear Time Series"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:54Z"}