Global temperature change is an important indicator of climate change. Climate time series data are characterized by trend, seasonal/cyclical as well as irregular components. Adequately modeling these components cannot be overemphasized. In this paper, we have proposed an approach of modeling temperature data using semiparametric additive generalized linear model. We have derived a penalized maximum likelihood estimation of the additive component of the semiparametric generalized linear models, that is, of regression coefficients and smooth functions. A statistical modeling with real time series data set was conducted on temperature data. The study has provided indications on the gain of using semiparametric modeling in situations where a signal component can be additively decomposed in to trend, cyclical and irregular components. Thus, we recommend semiparametric additive penalized models as an option to fit time series data sets in modelling the different component with different functions to adequately explain the relation inherent in data.

Parametric modeling imposes rigid assumption on abstraction of physical characteristics of a phenomenon, which in case of model misspecification could give erroneous results. To address the drawbacks, efforts have been channeled on semi-parametric and nonparametric modeling and inference. This study focuses on constructing an estimator and consequently modeling a meteorological temperature time series first by constructing a penalized spline estimator based on cubic splines. The penalized spline estimator proposed, which are known to impose very minimal restrictions on estimation process, provides good fits to observed data with very attractive properties namely consistent as observed in values of the Mean Squared Error from the analysis. The results of our simulations compared favorably with the empirical analysis on average monthly meteorological temperature data obtained from Climate Knowledge Portal World Bank Organization on Ghana for periods 1901-2016.