Daily Precipitation Modeling by Discrete Autoregressive Moving Average Processes

Abstract

To account for the statistical dependence among the daily precipitation magnitudes and among the daily precipitation occurrence times, various models from the discrete autoregressive moving average (DARMA) family are constructed for and applied to the daily precipitation data in Indiana. The structure of the DARMA family is specified by the marginal distribution of independent identically distributed (i.i.d.) discrete random variables and by their random linear combination. A fundamental property of the DARMA family is that its correlation structure can be specified independently of its marginal density. The DARMA correlation structure remains invariant under transformation of the marginal density. This property is satisfied by the Indiana daily precipitation data, and it facilitates their modeling by the DARMA family of processes. It is shown that the Markov chain, a popular model for the daily precipitation sequences, is a specified model within DARMA family. The Indiana daily precipitation data is transformed into a multistate discrete precipitation sequence by discretizing the daily precipitation amount into a number of magnitude states. The stochastic process of the daily precipitation sequences is analyzed in terms of the locally stationary seasons defined within the paper. In each season the candidate DARMA models are identified in terms of the covariance function within the season. The parameter estimation of these candidate models is done by fitting their theoretical autocorrelation functions to their empirical counterparts, and the state probabilities are obtained through the multistate mean run lengths. The theoretical run‐length distributions of the candidate models are derived for each of the precipitation magnitude states, including the dry state. The goodness‐of‐fit tests of the candidate models and the best model selection are based on the theoretical multistate run‐length distributions of the daily precipitation data.Supplement (data, tables, calculations, etc.) is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, DC 20009. Document W84‐001; $2.50. Payment must accompany order.