Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The methods are applied to data observations measuring water flow in cubic feet per second collected monthly in Newport, TN from the French Broad River. Simulated data corresponding to typical time series cases are then used for comparison and further exploration.
","abstract_html":"<p>Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The methods are applied to data observations measuring water flow in cubic feet per second collected monthly in Newport, TN from the French Broad River. Simulated data corresponding to typical time series cases are then used for comparison and further exploration.</p>","abstract_has_math":false,"creators":["Allen, Jake"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-17T07:00:00Z","date_published":"2011-08-17T07:00:00Z","updated_at":"2026-07-24T02:20:14Z","subjects":["moving averages","French Broad River","X-11","phase-plane plots","Longitudinal Data Analysis and Time Series","Physical Sciences and Mathematics","Statistics and Probability"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1349","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Allen, Jake"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["1990-01-01T08:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-08-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["moving averages","French Broad River","X-11","phase-plane plots","Longitudinal Data Analysis and Time Series","Physical Sciences and Mathematics","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/2540/viewcontent/AllenJ072511f.pdf","https://dc.etsu.edu/etd/1349"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The methods are applied to data observations measuring water flow in cubic feet per second collected monthly in Newport, TN from the French Broad River. Simulated data corresponding to typical time series cases are then used for comparison and further exploration.
"]},{"key":"dc:title","label":"Title","values":["Comparison of Time Series and Functional Data Analysis for the Study of Seasonality."]}]}],"canonical_facts":{"dc:creator":["Allen, Jake"],"dc:date.available":["1990-01-01T08:00:00Z"],"dc:date.issued":["2011-08-17T07:00:00Z"],"dc:description.abstract":["Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The methods are applied to data observations measuring water flow in cubic feet per second collected monthly in Newport, TN from the French Broad River. Simulated data corresponding to typical time series cases are then used for comparison and further exploration.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2540/viewcontent/AllenJ072511f.pdf","https://dc.etsu.edu/etd/1349"],"dc:rights":["Copyright by the authors."],"dc:subject":["moving averages","French Broad River","X-11","phase-plane plots","Longitudinal Data Analysis and Time Series","Physical Sciences and Mathematics","Statistics and Probability"],"dc:title":["Comparison of Time Series and Functional Data Analysis for the Study of Seasonality."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:20:14Z"}