The Markovian arrival process: A statistical model for daily precipitation amounts

•We examine the Markovian arrival process for modeling daily precipitation data.•The model captures the marginal statistical pattern and the empirical ACF.•We present a straightforward statistical method for estimation of the process.•We illustrate the performance of our approach on the base of 44 real series.•The outperformance of the MAP is shown in comparison to competing approaches.

The Markovian arrival process (MAP) is a stochastic process that allows for modeling dependent and non-exponentially distributed observations. Due to its versatility, it has been widely applied in different contexts, from reliability to teletraffic. In this work we show the suitability of the MAP for modeling daily precipitation data, which are often characterized by a non-negligible correlation structure. Specifically, a set of daily precipitation amounts series from the region of Andalusia (Spain) is shown to be correctly fitted with a two-state MAP.