Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Member

Dr. Robert Lund, Committee Chair

Committee Member

Dr. Peter Kiessler

Committee Member

Dr. Colin Gallagher

Committee Member

Dr. Xiaoqian Sun


Climatological time series are often periodically and spatially correlated. High dimensionality issues arise when modeling periodically and spatially correlated time series data "“ often, even simple multivariate models have more parameters than data points. This dissertation develops parsimonious methods for fitting periodically and spatially correlated multivariate time series data. Parsimonious VAR (vector autoregressive) and PVAR (periodic VAR) models are pursued here. The layered procedure introduced by Lund et al. (1995) is adopted as a basic scheme, which removes periodic correlation from the data in the first layer, and fits a stationary VAR model in the second layer. The method is applied to a daily maximum temperature data set of seven cities in southeastern U.S.. In addition, a portmanteau test is proposed for diagnosing serial correlations in periodic multivariate residuals. The performance of the test is examined in simulated data.