  We present a magnetic activity study of GJ 436 using spectroscopic data from
HARPS, spanning over 14 years, and additional data from NARVAL, falling within
the HARPS observations. We study the CaII H&K, HeID3, NaI doublet, H$\alpha$
and CaII IRT triplets lines and explore linear correlations between them. Using
the full HARPS dataset, we found indices H$\alpha$ vs CaII H&K & H$\alpha$ vs
HeI to correlate positively. From the NARVAL dataset, covering one observing
epoch, we found CaII IRT$_{3}$ vs CaII IRT$_{2}$ & CaII IRT$_{3}$ vs H$\alpha$
index to correlate negatively. We investigate long and short-term periodicity
in these index variations using the Generalised Lomb-Scargle periodogram. For
CaII H&K, NaI and H$\alpha$ indices, we detect long-term periods of 2470.7d (~
6.8 years), 1861.6d (~ 5.1 years) and 2160.9d (~ 5.9 years) respectively,
consistent with GJ 436's photometric cycle of ~ 7.4 years. Applying the "Pooled
Variance" technique to H$\alpha$ & NaI indices, we found ~ 2500d to be the
period of an activity cycle mechanism, in good agreement with the detected
2470.7d period. For CaII H&K and H$\alpha$ indices, we detect short-term
periods of $39.47^{+0.11}_{-0.15}$d and $40.46^{+0.44}_{-0.52}$d respectively,
identified as the stellar rotation period. The stellar rotation is detected
after prewhitening the long-term periodicity. It is detected as well in the
analysis of individual observing epochs.
