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Recent studies have revealed a hitherto unknown complexity of Cepheidpulsation. We implement local kernel regression to search for both period andamplitude modulations simultaneously in continuous time and to investigatetheir detectability, and test this new method on 53 classical Cepheids from theOGLE-III catalog. We determine confidence intervals using parametric andnon-parametric bootstrap sampling to estimate significance and investigatemulti-periodicity using a modified pre-whitening approach that relies ontime-dependent light curve parameters. We find a wide variety of period andamplitude modulations and confirm that first overtone pulsators are less stablethan fundamental mode Cepheids. Significant temporal variations in period aremore frequently detected than those in amplitude. We find a range of modulationintensities, suggesting that both amplitude and period modulations areubiquitous among Cepheids. Over the 12-year baseline offered by OGLE-III, wefind that period changes are often non-linear, sometimes cyclic, suggestingphysical origins beyond secular evolution. Our method more efficiently detectsmodulations (period and amplitude) than conventional methods reliant onpre-whitening with constant light curve parameters and more accuratelypre-whitens time series, removing spurious secondary peaks effectively.

Investigating Light Curve Modulation via Kernel Smoothing. I. Application to 53 fundamental mode and first-overtone Cepheids in the LMC