We present the first results obtained by the application of the KYNREFREV-reverberation model, which is ready for its use in XSPEC. This model computes the time dependent reflection spectra of the disc as a response to a flash of primary power-law radiation from a point source corona located on the axis of the black hole accretion disc (lamp-post geometry). Full relativistic effects are taken into account. The ionisation of the disc is set for each radius according to the amount of the incident primary flux and the density of the accretion disc. We tested the model by fitting model predictions to the observed time-lag spectra of three Narrow-Line Seyfert 1 galaxies (ARK 564, MCG-6-30-15 and 1H 0707-495), assuming either a rapidly or zero spinning black hole (BH). The time-lags strongly suggest a compact X-ray source, located close to the BH, at a height of approx. 4 gravitational radii. This result does not depend either on the BH spin or the disc ionization. There is no significant statistical difference between the quality of the best-fits in the rapidly and zero spinning BH scenarios in Ark 564 and MCG-6-30-15. But there is an indication that the hypothesis of a non-rotating BH in 1H 0707-495 is not consistent with its time-lag spectrum. Finally, the best-fits to the Ark 564 and 1H 0707-495 data are of rather low quality. We detect wavy-residuals around the best-fit reverberation model time-lags at high frequencies. This result suggests that the simple lamp-post geometry does not fully explain the X-ray source/disc configuration in Active Galactic Nuclei.
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