We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy, or a more sophisticated version that includes some price dynamics. We show that real market data can be surprisingly well accounted for by these simple models.