A comprehensive, but simple-to-use software package for analysis of time-series has been developed for paleoclimate research and education. Acycle runs either in the MATLAB environment or as a stand-alone application on Windows and Macintosh OS X, and is available free of charge. Acycle provides prewhitening procedures with multiple options available to track or remove secular trends, and integrates various power spectral analysis approaches for detection and tracking of periodic signals. Acycle also provides a toolbox that evaluates astronomical signals in paleoclimate series, and estimates the most likely sedimentation rate by maximizing the correlation coefficient between power spectra of an astronomical solution and a paleoclimate series. Sedimentary noise models for sea-level variations are also included. Many of the functions are specific to cyclostratigraphy and astrochronology, and are not found in standard, statistical packages. For a demonstration, Acycle is applied to a paleoclimate series (iron content) from Core BH9/05 in the Paleogene Central Basin of Svalbard that samples the Paleocene-Eocene Thermal Maximum (PETM). Acycle detects significant astronomical forcing of the iron series and demonstrates a relatively stable sedimentation rate during and after the PETM event.