Beta meteorological time series: application to air humidity data

Time series models are often used in the analysis of Meteorological phenomena to model levels of rainfall, temperature and levels of air humidity series in order to make forecasting and generate synthetic series which are inputs for the analysis of the influence of these variables on the quality of life. Relative air humidity for example, has great influence on the count increasing of respiratory diseases, especially for some age populations as newly born and elderly people. In this paper we introduce a new modeling approach for meteorological time series assuming a beta distribution for the data, where both the mean and precision parameters are being modeled. Bayesian methods using standard MCMC (Markov Chain Monte Carlo Methods) are used to simulate samples for the joint posterior distribution of interest. An example is given with a time series of 313 air humidity observations, measured by a wether station of Rio Claro, a city localized in S˜ao Paulo state, southeastern of Brazil