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. ^

Treefrogs in Forested Swamps at the La Selva Biological Station: Assemblage Variation through Space and Time

Swamp-breeding treefrogs form conspicuous components of many tropical forest sites, yet remain largely understudied. The La Selva Biological Station, a rainforest reserve in Costa Rica, harbors a rich swamp-breeding treefrog fauna that has been studied in only one of the many swamps found at the site. To understand if the species composition of treefrogs at La Selva varies over space or time, frogs were censused in 1982-83, 1994-95, 2005 and 2011 at two ponds located in the reserve. Data on treefrog habitat utilization were also collected. Species composition varied spatially only in 2011. Temporal variation was observed at both ponds for all groups tested. Habitat use varied among species and between swamps. The pattern of variation suggests that temporally dynamic systems such as temporary Neotropical forest swamps will converge and diverge in species composition over time.