FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS OF DAILY BIKE-SHARING DEMAND CURVES IN SEOUL: ASSOCIATIONS WITH SEASON, WEEKENDS AND HOLIDAYS

Bike-sharing demand is usually modeled as hourly counts, which hides the shape of the daily profile. We aimed to identify which daily-curve components differ by season, holiday and weekend, and whether a holiday effect remains after adjustment for weekend, temperature and rain. We analyzed 8,760 hourly Seoul rental records (1 December 2017 to 30 November 2018); removing 13 outage days left 352 daily curves. Curves were smoothed with a Fourier basis and summarized by functional principal component analysis (FPCA). Scores on the first three components (PC1 to PC3) were compared with rank-based tests and adjusted linear models with heteroscedasticity-consistent standard errors. Sensitivity analyses included a corrected holiday calendar and log(1 + count) curves. Three components carried 95.5% of the variance (PC1 82.7%). PC1 measured overall level, differed by season (ϵ²= 0.509) and rose with temperature (Spearman ρ = 0.72). PC2 contrasted commute peaks with an afternoon hump and separated weekends from weekdays (rank-biserial correlation 0.89). After adjustment, holidays were associated with a shift towards the weekend shape on PC2 (+698.5 score units, p = 0.0011; +920.7 with the corrected holiday flag). This was not detected on log(1 + count) curves, so it describes absolute and not proportional curve shape. The holiday effect on level was not established under the corrected flag. In one city over one year, demand level was associated with season and temperature, and demand shape with weekends and holidays. These are associations, not causal effects.