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.

Navigation Map of Douglas Reservoir-French Broad River published in 1952 by the Tennessee Valley Authority, Maps and Surveys Branch. Sheet 1 of a series of 3 maps covering Douglas Reservoir. This sheet covers mile 28.5 to mile 40.4. The index for the 3 map series can be found in the lower right quadrant. The legend denotes several information items pertaining to lake levels, direction of flow, roads, bridges, and other points of interest. Physical copy resides in the Government Information, Law and Maps Department of East Tennessee State University’s Sherrod Library. Scale: 1" = .5 mile. Datum is mean sea level / https://dc.etsu.edu/rare-maps/1030/thumbnail.jpg

Navigation Map of Douglas Reservoir-French Broad River published in 1952 by the Tennessee Valley Authority, Maps and Surveys Branch. Sheet 2 of a series of 3 maps covering Douglas Reservoir. This sheet covers mile 40.4 to mile 57.2. The index for the 3 map series can be found in the lower right quadrant. The legend denotes several information items pertaining to lake levels, direction of flow, roads, bridges, and other points of interest. Physical copy resides in the Government Information, Law and Maps Department of East Tennessee State University’s Sherrod Library. Scale: 1" = .5 mile. Datum is mean sea level. / https://dc.etsu.edu/rare-maps/1031/thumbnail.jpg

Soil Association map of the Upper French Broad River Watershed published in 1962 by the Tennessee Valley Authority, Division of Water Control Planning. Soil data supplied by Soils Department, North Carolina State College. Legend includes dominant soil type and descriptions, watershed divides, various types of roads, and other relevant information. Road names, mountains, communities, county lines, and other points of interest are also labeled on the map itself. Physical copy resides in the Government Information, Law and Maps Department of East Tennessee State University’s Sherrod Library. Scale: 2.5" = 10 miles / https://dc.etsu.edu/rare-maps/1033/thumbnail.jpg