A Framework For Spatiotemporal Prediction With Small And Heterogeneous Data And An Application To Consumer Price Indexes PDF Download

Spatio-temporal data analysis has been a hot topic in the recent statistical literature. In particular, there have been many developments in the study of spatio-temporal modelling. However, the development of spatio-temporal imputation and prediction is still limited. This thesis aims to propose new and better techniques for missing value imputation, modelling and prediction in the field of spatio-temporal analysis. The first contribution of this thesis is to propose a new method, designated CUTOFF, for imputing missing values in spatio-temporal data. The proposed method, named CUTOFF, is a linear estimator that utilises both spatial and temporal information in a spatio-temporal data matrix to impute missing values. Extensions are developed for this method to accommodate different data generating processes. CUTOFF is applied to impute missing values in the monthly rainfall data from the Murray-Darling Basin in Australia. CUTOFF is compared with four competing methods by cross-validation and simulation. It is shown that CUTOFF is superior to four competing methods in terms of imputation accuracy and computational efficiency. The second contribution of this thesis is to propose a general imputation framework that utilises variable selection methods to impute missing values. This framework is general in the sense that, firstly, variable selection plays a key role in the imputation, so many variable selection methods are incorporated into the framework; secondly, it not only can be used for data sets with only numerical variables, other data sets with only categorical variables and mixed-type variables can also be imputed within the framework. Using real data sets and simulation, it is demonstrated that variable selection methods can be used in the proposed framework to impute missing values. The convergence property of the proposed imputation framework is also examined. The third contribution is to propose a spatio-temporal model to analyse the Murray-Darling Basin rainfall data, and to be used for spatial and short-term temporal prediction. A spatio-temporal dummy approach is proposed in the model to deal with the zero-inflation problem in the data. An ensemble prediction technique is proposed to achieve out-sample temporal prediction. Using the spatio-temporal dummy as a key covariate in the model, the out-sample spatial prediction accuracy is demonstrated to be improved significantly and consistently. The proposed ensemble prediction technique allows the short-term out-sample temporal prediction to be done when there is a spatio-temporal dummy in the model, and the prediction accuracy by such a model is better than most univariate time series models. Finally, two R packages have been developed to support the two imputation methods proposed. The first R package cutoffR corresponds to the fist contribution, including the implementation of the CUTOFF algorithm, the CUTOFF extensions, the cross-validation and simulation, and some useful tools for spatio-temporal imputation study. The second R package imputeR corresponds to the second contribution where a general imputation framework proposed is proposed. Both packages are freely available on CRAN (http://cran.r-project.org/).