Multi-band Variability Analysis of Mrk 421

We have assembled the historical variability data of Mrk 421 at radio 15 GHz, X-ray and gamma-ray bands, spanning about 6.3, 10.3 and 7.5 yr, respective- ly. We analyzed the variability by using three methods. The results indicated that there is a period of 287.6 +- 4.4 days for 15 GHz, 309.5 +- 5.8 days for X- ray and 283.4+- 4.7 days for gamma-ray, respectively. This period can be reasonably explained by the nonballistic helical motion of the emitting material. The cor- relation analysis suggested that the variabilities of radio 15 GHz, X-ray and 0-ray are remarkable correlated, and the emission of radio 15 GHz lags behind that of X-ray, and the X-ray flux lags behind the gamma-ray. This suggests that the gamma-ray derives from inverse Compton (IC) scattering of the synchrotron photons, supporting the synchrotron self-Compton (SSC) model. Moreover, the time delay between different wavebands could be explained by the shock-in-jet models, in which a moving emission region produces the radio to gamma-ray activity, implying that the emission region of gamma-ray is closer to the center than ones of X-ray and radio emission.