In the thesis, we introduced the basic characters of active galactic nuclei and blazar and radiative model. We mainly investigated the variability of blazar and many methods detecting light period including the Jurkevich method, the power spectral method and the discrete autocorrelation function(DACF) method. We confirmed three methods are feasible using calculating period of discrete observation data by digital simulation. And we were looked for their similarities and differences.We calculated and analysed light period for QSO PKS1510-089at radio waveband and optical R band by applying the above three methods. The data of R band was from our long-term observation and literature. And the data of radio band was collected from literature. According to integrating analysis of three methods, the credible periodicities are0.9yr(year) at37GHz,0.95yr at22GHz,1.Oyr at R band in PKS1510-089. And we think the period is approximately1.Oyr at radio band and optical band of the source.We studied color index using the simultaneous multi-band(B V R I)observation data of three blazars OJ248,3C66A and PKS0716+714. We found OJ248has strong correlation between color index and magnitude;3C66A has strong correlation be-tween color index V-R and magnitude R, but the others have almost no correlation; PKS0716+714has very week correlation between color index and magnitude. And when the three sources turn brighter the spectrum becomes bluer(flatter). |