Context : NGC 5408 X-1 is one of the few ultraluminous X-ray sources ( ULXs ) with an extensive monitoring program in X-rays ( a temporal baseline of 4.2 yr ) , making it one of the most suitable candidates to study the long-timescale quasi-periodic oscillations ( QPOs ) .

Aims : Previous timing analysis of the Swift data of NGC 5408 X-1 led to detection of multiple periodicities ranging from 2.6 d to 230 d. In this paper , we focus on the statistical significance and the temporal evolution of these periodicities .

Methods : A time-series analysis technique in the time-frequency domain , the weighted wavelet Z -transform ( WWZ ) , was employed to identify the periodicities and trace their variations with time .

Results : Three periodic components were detected from the WWZ periodogram , corresponding to periods of 2.65 \pm 0.01 d , 115.4 \pm 14.4 d and 189.1 \pm 15.2 d. All three have statistical significance higher than 99.74 % ( \gtrsim 3 \sigma ) .
The 2.65-d periodicity is quite stable in the majority of the light curve , whereas it changes to a shorter 2.50 d period in the last third of the time interval covered by the light curve .
The 115-d periodicity is the most prominent but appears variable .
It starts at an initial value of \sim 117.8 d and reaches 115.4 d around MJD 54800 ; then it shifts into a lower-frequency branch ( 136 d period ) between MJD 55200 – 55750 ; after that , this periodicity returns to 115 d until the end of the monitoring period .
The 189-d periodicity is persistent across the whole time coverage .
It shows a steadily decreasing trend from the beginning ( 193 d period ) to the end ( 181 d period ) .

Conclusions : The long-timescale periodicities in NGC 5408 X-1 are most likely of super-orbital origin , and are probably associated with the precession of a warped accretion disc .
The disc may have been broken into two distinct planes with different precessing periods , i.e .
the 189-d and 115-d periodicities corresponding to the outer and inner disc , respectively .