  Aims. Hot Jupiters are thought to belong to single-planet systems. Somewhat
surprisingly, some hot Jupiters have been reported to exhibit transit timing
variations (TTVs). The aim of this paper is to identify the origin of these
observations, identify possible periodic biases leading to false TTV
detections, and refine the sample to a few candidates with likely dynamical
TTVs. Methods. We present TTV frequencies and amplitudes of hot Jupiters in
Kepler Q0--6 data with Fourier analysis and a frequency-dependent bootstrap
calculation to assess the false alarm probability levels of the detections.
Results. We identified 36 systems with TTV above four standard deviation
confidence, about half of them exhibiting multiple TTV frequencies. Fifteen of
these objects (HAT-P-7b, KOI-13, 127, 183, 188, 190, 196, 225, 254, 428, 607,
609, 684, 774, 1176) probably show TTVs due to a systematic observational
effect: long cadence data sampling is regularly shifted transit-by-transit,
interacting with the transit light curves, introducing a periodic bias, and
leading to a stroboscopic period. For other systems, the activity and rotation
of the host star can modulate light curves and explain the observed TTVs. By
excluding the systems that were inadequately sampled, showed TTV periods
related to the stellar rotation, or turned out to be false positives or
suspects, we ended up with seven systems. Three of them (KOI-186, 897, 977)
show the weakest stellar rotation features, and these are our best candidates
for dynamically induced TTV variations. Conclusions. Those systems with
periodic TTVs that we cannot explain with systematics from observation, stellar
rotation, activity, or inadequate sampling may be multiple systems or even
exomoon hosts.
