Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Temporal analysis of land use and transportation investments with geographic information system

Land use and transportation interaction has been a research topic for several decades. There have been efforts to identify impacts of transportation on land use from several different perspectives. One focus has been the role of transportation improvements in encouraging new land developments or relocation of activities due to improved accessibility. The impacts studied have included property values and increased development. Another focus has been on the changes in travel behavior due to better mobility and accessibility. Most studies to date have been conducted in metropolitan level, thus unable to account for interactions spatially and temporally at smaller geographic scales. ^ In this study, a framework for studying the temporal interactions between transportation and land use was proposed and applied to three selected corridor areas in Miami-Dade County, Florida. The framework consists of two parts: one is developing of temporal data and the other is applying time series analysis to this temporal data to identify their dynamic interactions. Temporal GIS databases were constructed and used to compile building permit data and transportation improvement projects. Two types of time series analysis approaches were utilized: univariate models and multivariate models. Time series analysis is designed to describe the dynamic consequences of time series by developing models and forecasting the future of the system based on historical trends. Model estimation results from the selected corridors were then compared. ^ It was found that the time series models predicted residential development better than commercial development. It was also found that results from three study corridors varied in terms of the magnitude of impacts, length of lags, significance of the variables, and the model structure. Long-run effect or cumulated impact of transportation improvement on land developments was also measured with time series techniques. The study offered evidence that congestion negatively impacted development and transportation investments encouraged land development. ^