We present the results of our power spectral density analysis for the BL Lac object OJ 287, utilizing the Fermi-LAT survey at high-energy γ-rays, Swift-XRT in X-rays, several ground-based telescopes and the Kepler satellite in the optical, and radio telescopes at GHz frequencies. The light curves are modeled in terms of continuous-time autoregressive moving average (CARMA) processes. Owing to the inclusion of the Kepler data, we were able to construct for the first time the optical variability power spectrum of a blazar without any gaps across ∼6 dex in temporal frequencies. Our analysis reveals that the radio power spectra are of a colored-noise type on timescales ranging from tens of years down to months, with no evidence for breaks or other spectral features. The overall optical power spectrum is also consistent with a colored noise on the variability timescales ranging from 117 years down to hours, with no hints of any quasi-periodic oscillations. The X-ray power spectrum resembles the radio and optical power spectra on the analogous timescales ranging from tens of years down to months. Finally, the γ-ray power spectrum is noticeably different from the radio, optical, and X-ray power spectra of the source: we have detected a characteristic relaxation timescale in the Fermi-LAT data, corresponding to ∼150 days, such that on timescales longer than this, the power spectrum is consistent with uncorrelated (white) noise, while on shorter variability timescales there is correlated (colored) noise.