Recent multi-band variability studies have revealed that active galactic nucleus (AGN) accretion disc sizes are generally larger than the predictions of the classical thin disc by a factor of $2sim 3$. This hints at some missing key ingredient in the classical thin disc theory: here, we propose an accretion disc wind. For a given bolometric luminosity, in the outer part of an accretion disc, the effective temperature in the wind case is higher than that in the no-wind one; meanwhile, the radial temperature profile of the wind case is shallower than the no-wind one. In presence of winds, for a given band, blackbody emission from large radii can contribute more to the observed luminosity than the no-wind case. Therefore, the disc sizes of the wind case can be larger than those of the no-wind case. We demonstrate that a model with the accretion rate scaling as $dot{M}_0 (R/R_{mathrm{S}})^{beta}$ (i.e., the accretion rate declines with decreasing radius due to winds) can match both the inter-band time lags and the spectral energy distribution of NGC 5548. Our model can also explain the inter-band time lags of other sources. Therefore, our model can help decipher current and future continuum reverberation mapping observations.
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