Modelling sea surface temperature using generalized additive models for location scale and shape by boosting with autocorrelation

Sea surface temperature (SST) is one of many important parameters that influence the climate system of the earth. Modelling of and prediction from the SST data are challenging due to the fact that gaps in the data lead to incomplete information over time. Generalized additive models by boosting with location scale and shape (gamboostLSS) can be applied to overcome this problem. Moreover, they also deal with sparsity, irregular peaks, and autocorrelation in the data. We propose in this thesis extended gamboostLSS models by considering time autocorrelation. In our experiments, we initially used 1231 daily observations in the period between November 2006 and September 2012. The data is then further extended from three different moored buoys. The data consisting of the SST as the response from buoys in the Indian Ocean and the air temperature (in Celsius), humidity (in percentage) and rainfall (in millimetre) covariates are considered from land stations in Sumatra Island. Removing autocorrelation with an AR(1) model has a large impact on global and local model fitting. GamboostLSS-AR(1) models are an advanced technique for removing autocorrelation. We also computed marginal prediction interval with autocorrelation (MPIAR(1)) of the model. MPI-AR(1) of the gamboost LSS-AR(1) model can be used to predict the missing data in various gaps and to obtain a prediction interval of submodels. The MPI-AR(1) that is applied to different buoys indicated that gamboost LSS-AR(1) model fitting is better than MPI by gamboost LSS model with and without transformation of rainfall. The MPI-AR(1) is more flexible to follow the pattern of the SST data fitting. Our proposed gamboost LSS-AR(1) models are more flexible, interpretable and capable to handle missing data, as well as to deal with high dimensional data and capture complex data structures.