The objective of this work is to model statistically the ultraviolet radiation index (UV Index) to make forecast (extrapolate) and analyze trends. The task is relevant, due to increased UV flux and high rate of cases non-melanoma skin cancer in northeast of Brazil. The methodology utilized an Autoregressive Distributed Lag model (ADL) or Dynamic Linear Regression model. The monthly data of UV index were measured in east coast of the Brazilian Northeast (City of Natal-Rio Grande do Norte). The Total Ozone is single explanatory variable to model and was obtained from the TOMS and OMI/AURA instruments. The Predictive Mean Matching (PMM) method was used to complete the missing data of UV Index. The results mean squared error (MSE) between the observed UV index and interpolated data by model was of 0.36 and for extrapolation was of 0.30 with correlations of 0.90 and 0.91 respectively. The forecast/extrapolation performed by model for a climatological period (2012-2042) indicated a trend of increased UV (Seasonal Man-Kendall test scored τ = 0.955 and p-value < 0.001) if the Total Ozone remain on this tendency to reduce. In those circumstances, the model indicated an increase of almost one unit of UV index to year 2042.