We present the analysis of RXTE-PCA observations of GX 1+4 between 2001 March 3 and 2003 January 31 together with the CGRO-BATSE X-ray flux and frequency derivative time series between 1991 and 1999. From the timing analysis of RXTE-PCA observations, we are able to phase connect pulse arrival times of the source within two different time intervals and obtain corresponding timing solutions. Using these pulse arrival times, we contribute to long-term pulse frequency history of the source. We look for episodic correlations and anti-correlations between the torque and X-ray luminosity using the CGRO-BATSE X-ray flux and frequency derivative time series and find that the correlation state of GX 1+ 4 seems to change on similar to 100-200 d long intervals. We estimate the torque noise of the source and observe the flickering noise (f(-1)). We measure the longest observed time-scale for a noise process amongst accretion-powered X-ray pulsars by extending the noise estimate for a time-scale ranging from 31 d to 44 yr. Spectral analysis of individual RXTE-PCA observations indicates a significant correlation between the iron line flux and the unabsorbed X-ray flux. Pulse-phase-resolved spectra of the source indicate a broadening of iron line complex at the bin corresponding to the pulse minimum.