  We present our statistical study of near infrared (NIR) variability of X-ray
selected Active Galactic Nuclei (AGN) in the COSMOS field, using UltraVISTA
data. This is the largest sample of AGN light curves in YJHKs bands, making
possible to have a global description of the nature of AGN for a large range of
redshifts, and for different levels of obscuration. To characterize the
variability properties of the sources we computed the Structure Function. Our
results show that there is an anti-correlation between the Structure Function
$A$ parameter (variability amplitude) and the wavelength of emission, and a
weak anti-correlation between $A$ and the bolometric luminosity. We find that
Broad Line (BL) AGN have a considerably larger fraction of variable sources
than Narrow Line (NL) AGN, and that they have different distributions of the
$A$ parameter. We find evidence that suggests that most of the low luminosity
variable NL sources correspond to BL AGN, where the host galaxy could be
damping the variability signal. For high luminosity variable NL, we propose
that they can be examples of "True type II" AGN or BL AGN with limited spectral
coverage which results in missing the Broad Line emission. We also find that
the fraction of variable sources classified as unobscured in the X-ray is
smaller than the fraction of variable sources unobscured in the optical range.
We present evidence that this is related to the differences in the origin of
the obscuration in the optical and X-ray regimes.
