Does volatility reflect lasting reactions to past shocks or changes in the markets induce shifts in this variable dynamics? In this work, we argue that price variations are an essential source of information about multiple regimes in the realized volatility of stocks, with large falls (rises) in prices bringing persistent regimes of high (low) variance. The study shows that this asymmetric effect is highly significant (we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20% and 60% higher than the average of periods with stable or rising prices) and support large empirical values of long memory parameter estimates. We show that a model based on those findings significantly improves out of sample performance in relation to standard methods {specially in periods of high volatility.