Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Kevin D. Robbins


The major objective of this research is to develop daily time series models for maximum and minimum temperature series. A generalized modeling methodology is presented. Stochastic modeling was accomplished by analyzing the structural characteristics of the temperature series. Analyses included assessment for time reversibility, linearity, structural dependence and distributional properties of the weakly stationary series obtained by parametric standardization of the observed series. Based on the results of the structural characterization of the series and the results of the model class identification using a 'state-dependent model' formulation, a bilinear model class was identified as appropriate for the temperature series. Various bilinear models were explored and, for comparison, linear ARMA models were also fitted. Diagnostic checks for model adequacy indicated that the BL(1,1,1,1) model is appropriate for the temperature series. Data simulation was used to validate the selected bilinear model. Results were compared to that of an ARMA(1,1) model. Results indicated that a bilinear model is marginally better than a linear ARMA model in simulating the daily means and variances of the observed series. However, the bilinear model is capable of preserving the nonlinearity in the observed series. The ARMA model simulated a linear series. The BL(1,1,1,1) model was fitted to 49 stations in Louisiana and 15 stations along the borders of Texas, Arkansas and Mississippi. A geostatistical approach was used to analyze the spatial distribution of the Fourier coefficients describing the seasonal variation of the daily means and standard deviations and the parameters of the bilinear model. Results indicated that the parameters show a general latitudinal trend. There is either a N-S or NW-SE drift in the parameters. This is more pronounced in the Fourier coefficients. Structural analysis of the de-trended spatial series of the parameters was performed. Semivariogram analyses of the parameters showed that an exponential, linear, or constant semivariogram model is appropriate for the Fourier coefficients. On the other hand, either a linear or constant semivariogram model is appropriate for the bilinear model coefficients. Ordinary kriging was validated as an interpolation routine for obtaining model parameters at an ungaged site. Parameters for seven stations were interpolated and data simulation was performed using the estimated parameters. Results were compared with results of simulation using parameters that are considered as regional constants. Simulation results using kriged parameters were better than using parameters as regional constants.