  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 $2\sim 3$. 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.
