three aperiodic PSD models. The current baseline of the observed database is 43 years, corresponding to a $\sim3.3\sigma$ confidence level (see Section 4.3). Under the observation configurations described above, an additional monitoring period of $\sim$30-60 years (about 1.5-3 cycles) is required to reach a $5\sigma$ confidence level (equivalent to a false alarm probability of $6\times10^{-7}$). We stress that the adopted observation configurations are quite conservative and therefore the obtained monitoring length is just a conservative estimate. Higher data quality (e.g., higher signal to noise ratio and smaller seasonal gap) may reduce the required monitoring length.

![Two examples of the extraction of the broad H$\beta$ profile. The top panel shows the mean spectrum of our Lijiang observations between 2016 and 2017. The bottom panel shows the historical spectrum from November 22, 1976 digitalized from [@Carpriotti1982], which has narrow wavelength coverage.[]{data-label="fig_decomp"}](spec_decomp.pdf){width="48.00000%"}

![(Left) H$\beta$ profiles from 1976 to 2017. (Right) Folded H$\beta$ profile series with phases for a complete cycle using a period [of]{} 20.5 years. Black lines represent the overall mean profiles of each phase. Blue and red lines represent profiles from the first and second cycles of the series respectively. Vertical lines show the wavelength center of [the]{} H$\beta$ line.[]{data-label="fig_prof"}](prof_all.pdf){width="45.00000%"}

H$\beta$ 