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To investigate the variability of the star formation rate (SFR) of galaxies,we define a star formation change parameter, SFR$_{\rm 5Myr}$/SFR$_{\rm800Myr}$ which is the ratio of the SFR averaged within the last 5 Myr to theSFR averaged within the last 800 Myr. We show that this parameter can bedetermined from a combination of H$\alpha$ emission and H$\delta$ absorption,plus the 4000 A break, with an uncertainty of $\sim$0.07 dex for star-forminggalaxies. We then apply this estimator to MaNGA galaxies, both globally withinRe and within radial annuli. We find that galaxies with higher global SFR$_{\rm5Myr}$/SFR$_{\rm 800Myr}$ appear to have higher SFR$_{\rm 5Myr}$/SFR$_{\rm800Myr}$ at all galactic radii, i.e. that galaxies with a recent temporalenhancement in overall SFR have enhanced star formation at all galactic radii.The dispersion of the SFR$_{\rm 5Myr}$/SFR$_{\rm 800Myr}$ at a given relativegalactic radius and a given stellar mass decreases with the (indirectlyinferred) gas depletion time: locations with short gas depletion time appear toundergo bigger variations in their star-formation rates on Gyr or lesstimescales. In Wang et al. (2019) we showed that the dispersion instar-formation rate surface densities $\Sigma_{\rm SFR}$ in the galaxypopulation appears to be inversely correlated with the inferred gas depletiontimescale and interpreted this in terms of the dynamical response of agas-regulator system to changes in the gas inflow rate. In this paper, we cannow prove directly with SFR$_{\rm 5Myr}$/SFR$_{\rm 800Myr}$ that these effectsare indeed due to genuine temporal variations in the SFR of individual galaxieson timescales between $10^7$ and $10^9$ years rather than possibly reflectingintrinsic, non-temporal, differences between different galaxies.

The Variability of the Star Formation Rate in Galaxies: I. Star Formation Histories Traced by EW(H$\alpha$) and EW(H$\delta_A$)