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tokens: becomes more and more noisy toward higher frequencies and therefore the de-convolved power spectrum will be more and more uncertain toward higher and higher frequencies. Figure 15. (a) Simulated red-noise light curve ( a = 2), containing 1000 data points with a sampling interval of one day (blue open circles), along with 30% of the time series selected at random times to mimic an unevenly sampled data set (magenta stars). (b) The corresponding power spectra of the unevenly sampled light curve derived using the LSP method (resulting in a = 0.3; magenta dashed curve), and the FT of the ACF (returning a = −0.1; cyan dashed curve). (c) Spectral window of power spectrum estimated from FT of the ACF (see the text of Appendix A for details). Appendix B Selection of (<italic>p</italic>, <italic>q</italic>) Parameters for the CARMA Process The order of the CARMA( p , q ) process is chosen based on how close the model is to the data using the minimum AICc criterion adopted in the present study. It has been argued that the models for various pairs of ( p , q ) values for which the minimum AICc is within 10 are not statistically indistinguishable from each other. Figure 16 shows power spectra corresponding to a few sets of ( p , q ) parameters of the analyzed Fermi -LAT light curve. As these overlap substantially, we choose the lowest-order model—CARMA(1, 0)—as the best-fitting model to describe the high-energy γ –ray variability in OJ 287. Figure 16. Power spectra corresponding to a few sets of ( p , q ) parameters of the analyzed Fermi -LAT light curve of OJ 287. The corresponding 1 σ confidence intervals are denoted by shaded areas. See the text of Appendix B for details. Appendix C Lack of ∼12 Year QPO in the Optical Light Curve Here, we discuss in more detail the lack of the claimed ∼12 year quasi-periodicity in the analyzed optical light curve. To demonstrate the robustness of the CARMA modeling in detecting QPO features against the background of red noise in the power spectrum for a finite time series covering only a few periods, an artificial light curve is generated with three components: (1) a pure red-noise ( β = 2) power spectrum using the method of Emmanoulopoulos et al. ( 2013 ), (2) a sinusoidal component with a 12 year period, and (3) a Gaussian white noise with mean 0 and standard deviation 0.1 representing measurement uncertainty. The data points are evenly sampled with a sampling interval of 1 day, and the total duration of the simulated time series is 14,600 days (40 years, corresponding to our relatively better sampled optical light curve starting from 1970; see Table 2 ). Next, we kept 20% of the data selected at random times to mimic an unevenly sampled data set. Figures 17 (a)–(e) present the results of CARMA modeling on our simulated light curve, while Figure 17 (f) shows the computed power spectrum. Since the simulated light curve covers only ∼3 periods, we do not detect a clear peak on the ∼12 year timescale against the