the following assumptions: 1) the long-term variations are sinusoidal with the parameters given by the sinusoidal fitting in Section 4.1; and 2) the variations at short time scales follow a single power-law PSD with the parameters $\log A=-2.2\pm0.2$ and $\alpha=1.6\pm0.1$ from Section 3. The single power law is set to flatten to a constant below $1.0\times10^{-3}~{\rm day}^{-1}$ to confine the generated variations to short time scales. We generate a [artificial]{} light curve by summing up the above two variation components. Following the typical configurations of the observed data, the cadence of the [artificial]{} light curve is set to be 10 days apart and the seasonal gap is set to last three months. A Gaussian noise with a standard deviation of $0.37\times10^{-15}~\rm erg~s^{-1}~cm^{-2}~\text{\AA}^{-1}$ is added into the [artificial]{} light curve. One quarter of points are discarded to mimic bad weather or [instrumental]{} problems. We then attach the [artificial]{} light curve to the observed data and use this new [artificial]{} data to calculate the false alarm probability as in Section 4.3. Appendix B illustrates three examples of [artificial]{} light curves for Ark 120. In Figure \[fig\_fap\], we show the dependence of the estimated false alarm probability on the monitoring time length for 