This study focuses on how the construction of a paleoclimate time series influences the interpretation in the frequency domain. Three time series are examined: a New Caledonian coral (Amedee Island), a Chinese speleothem (Dongge Cave), and New Mexican trees (El Malpais). This study presents a monthly resolved coral Sr/Ca time series from New Caledonia that reconstructs sea surface temperature (SST; 1648-1999). The chronology is based on density-band counting, cross-correlating Sr/Ca, and ²³°Th dating. The intracolony coral Sr/Ca variations are coherent on interannual to centennial time scales and are reproducible for >300 years. The SST reconstruction reveals estimated cooling trend (~0.4°C) from 1741-1815, a colder nineteenth century (~0.6°C), and a warming trend (~0.6°C) in the twentieth century. Spectral and wavelet analysis reveals significant inter-decadal periodicities (~14-21 years/cycle) that modulate with time, and nearly persistent multi-decadal periodicities (~25-33 years/cycle) that do not exhibit coherence with the Inter-decadal Pacific Oscillation. The multi-decadal periodicities may be a harmonic of the inter-decadal periodicities or may represent an independent mode not previously recognized. The Dongge Cave time series is based on uneven time intervals between data points (∆t) requiring interpolation to a constant ∆t for analysis with traditional spectral methods. A comparison of the even and uneven ∆t spectra using the Lomb-Scargle transform reveals the interpolated spectrum contains suppressed periodicities (<20 years/cycle), in contrast to the uninterpolated spectrum, resulting in a steeper slope in the red noise model thus influencing significance testing. The El Malpais time series is an average of tree-ring width series. Spectral analysis of the entire time series identified significant periodicities. However, significance varies between three temporal subsets, in which the number of series varies; therefore, these periodicities may be a function of the number of series or may represent a real temporal variability. Cross-spectral analysis of the El Malpais and Dongge Cave time series reveals significant coherence; however, cross-wavelet analysis, which examines localized frequencies in the time domain, reveals a lack of correlation; therefore, coherence in the frequency domain does not indicate correlation in the time domain.