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. ^

Essays in open economy macroeconomics

Research macroeconomists have witnessed remarkable methodological developments in mathematical, statistical, and computational tools during the last two decades. The three essays in this dissertation took advantage of these advances to analyze important macroeconomic issues. ^ The first essay, “ Habit Formation, Adjustments Costs, and International Business Cycle Puzzles” analyzes the extent to which incorporating habit formation and adjustment costs in investment in a one-good two-country general equilibrium model would help overcome some of the international business cycle puzzles. Unlike standard results in the literature, the model generates persistent, cyclical adjustment paths in response to shocks. It also yields positive cross-country correlations in consumption, employment, investment, and output. Cross-country correlations in output are higher than the ones in consumption. This is qualitatively consistent with the stylized facts. These results are particularly striking given the predicted negative correlations in investment, employment, and output that are typically found in the literature. ^ The second essay, “Comparison Utility, Endogenous Time Preference, and Economic Growth,” uses World War II as a natural experiment to analyze the degree to which a model where consumers' preferences exhibit comparison-based utility and endogenous discounting is able to improve upon existing models in mimicking the transitional dynamics of an economy after a shock that destroys part of its capital stock. The model outperforms existing ones in replicating the behavior of the saving rate (both on impact and along the transient paths) after this historical event. This result brings additional support to the endogenous rate of time preference being a crucial element in growth models. ^ The last essay, “Monetary Policy under Fear of Floating: Modeling the Dominican Economy,” presents a small scale macroeconomic model for a country (Dominican Republic) characterized by a strong presence of fear of floating (reluctance to have a flexible exchange rate regime) in the conduct of monetary policy. The dynamic responses of this economy to external shocks that are of interest for monetary policy purposes are analyzed under two alternative interest rate policy rules: One being the standard Taylor rule and another that responds explicitly to deviations of the exchange rate with respect to its long-term trend. ^

Essays in Open Economy Macroeconomics

Research macroeconomists have witnessed remarkable methodological developments in mathematical, statistical, and computational tools during the last two decades. The three essays in this dissertation took advantage of these advances to analyze important macroeconomic issues. The first essay, “ Habit Formation, Adjustments Costs, and International Business Cycle Puzzles” analyzes the extent to which incorporating habit formation and adjustment costs in investment in a one-good two-country general equilibrium model would help overcome some of the international business cycle puzzles. Unlike standard results in the literature, the model generates persistent, cyclical adjustment paths in response to shocks. It also yields positive cross-country correlations in consumption, employment, investment, and output. Cross-country correlations in output are higher than the ones in consumption. This is qualitatively consistent with the stylized facts. These results are particularly striking given the predicted negative correlations in investment, employment, and output that are typically found in the literature. The second essay, “Comparison Utility, Endogenous Time Preference, and Economic Growth,” uses World War II as a natural experiment to analyze the degree to which a model where consumers' preferences exhibit comparison-based utility and endogenous discounting is able to improve upon existing models in mimicking the transitional dynamics of an economy after a shock that destroys part of its capital stock. The model outperforms existing ones in replicating the behavior of the saving rate (both on impact and along the transient paths) after this historical event. This result brings additional support to the endogenous rate of time preference being a crucial element in growth models. The last essay, “Monetary Policy under Fear of Floating: Modeling the Dominican Economy,” presents a small scale macroeconomic model for a country (Dominican Republic) characterized by a strong presence of fear of floating (reluctance to have a flexible exchange rate regime) in the conduct of monetary policy. The dynamic responses of this economy to external shocks that are of interest for monetary policy purposes are analyzed under two alternative interest rate policy rules: One being the standard Taylor rule and another that responds explicitly to deviations of the exchange rate with respect to its long-term trend.

Neuroendocrine control of a dynamic communication signal

Multiple physiological systems regulate the electric communication signal of the weakly electric gymnotiform fish, Brachyhypopomus pinnicaudatus. Fish were injected with neuroendocrine probes which identified pharmacologically relevant serotonin (5-HT) receptors similar to the mammalian 5-HT1AR and 5-HT2AR. Peptide hormones of the hypothalamic-pituitary-adrenal/interrenal axis also augment the electric waveform. These results indicate that the central serotonergic system interacts with the hypothalamic-pituitary-interrenal system to regulate communication signals in this species. The same neuroendocrine probes were tested in females before and after introducing androgens to examine the relationship between sex steroid hormones, the serotonergic system, melanocortin peptides, and EOD modulations. Androgens caused an increase in female B. pinnicaudatus responsiveness to other pharmacological challenges, particularly to the melanocortin peptide adrenocorticotropic hormone (ACTH). A forced social challenge paradigm was administered to determine if androgens are responsible for controlling the signal modulations these fish exhibit when they encounter conspecifics. Males and females responded similarly to this social challenge construct, however introducing androgens caused implanted females to produce more exaggerated responses. These results confirm that androgens enhance an individual's capacity to produce an exaggerated response to challenge, however another unidentified factor appears to regulate sex-specific behaviors in this species. These results suggest that the rapid electric waveform modulations B. pinnicaudatus produces in response to conspecifics are situation-specific and controlled by activation of different serotonin receptor types and the subsequent effect on release of pituitary hormones.

Dynamic modeling and analysis of single-stage boost inverters under normal and abnormal conditions

Inverters play key roles in connecting sustainable energy (SE) sources to the local loads and the ac grid. Although there has been a rapid expansion in the use of renewable sources in recent years, fundamental research, on the design of inverters that are specialized for use in these systems, is still needed. Recent advances in power electronics have led to proposing new topologies and switching patterns for single-stage power conversion, which are appropriate for SE sources and energy storage devices. The current source inverter (CSI) topology, along with a newly proposed switching pattern, is capable of converting the low dc voltage to the line ac in only one stage. Simple implementation and high reliability, together with the potential advantages of higher efficiency and lower cost, turns the so-called, single-stage boost inverter (SSBI), into a viable competitor to the existing SE-based power conversion technologies.^ The dynamic model is one of the most essential requirements for performance analysis and control design of any engineering system. Thus, in order to have satisfactory operation, it is necessary to derive a dynamic model for the SSBI system. However, because of the switching behavior and nonlinear elements involved, analysis of the SSBI is a complicated task.^ This research applies the state-space averaging technique to the SSBI to develop the state-space-averaged model of the SSBI under stand-alone and grid-connected modes of operation. Then, a small-signal model is derived by means of the perturbation and linearization method. An experimental hardware set-up, including a laboratory-scaled prototype SSBI, is built and the validity of the obtained models is verified through simulation and experiments. Finally, an eigenvalue sensitivity analysis is performed to investigate the stability and dynamic behavior of the SSBI system over a typical range of operation. ^

Aquatic fauna as indicators for Everglades restoration: Applying dynamic targets in assessments

A major goal of the Comprehensive Everglades Restoration Plan (CERP) is to recover historical (pre-drainage) wading bird rookeries and reverse marked decreases in wading bird nesting success in Everglades National Park. To assess efforts to restore wading birds, a trophic hypothesis was developed that proposes seasonal concentrations of small-fish and crustaceans (i.e., wading bird prey) were a key factor to historical wading bird success. Drainage of the Everglades has diminished these seasonal concentrations, leading to a decline in wading bird nesting and displacing them from their historical nesting locations. The trophic hypothesis predicts that restoring historical hydrological patterns to pre-drainage conditions will recover the timing and location of seasonally concentrated prey, ultimately restoring wading bird nesting and foraging to the southern Everglades. We identified a set of indicators using small-fish and crustaceans that can be predicted from hydrological targets and used to assess management success in regaining suitable wading bird foraging habitat. Small-fish and crustaceans are key components of the Everglades food web and are sensitive to hydrological management, track hydrological history with little time lag, and can be studied at the landscape scale. The seasonal hydrological variation of the Everglades that creates prey concentrations presents a challenge to interpreting monitoring data. To account for the variable hydrology of the Everglades in our assessment, we developed dynamic hydrological targets that respond to changes in prevailing regional rainfall. We also derived statistical relationships between density and hydrological drivers for species representing four different life-history responses to drought. Finally, we use these statistical relationships and hydrological targets to set restoration targets for prey density. We also describe a report-card methodology to communicate the results of model-based assessments for communication to a broad audience.

Survival and growth responses of eight Everglades tree species along an experimental hydrological gradient on two tree island types

Questions: How are the early survival and growth of seedlings of Everglades tree species planted in an experimental setting on artificial tree islands affected by hydrology and substrate type? What are the implications of these responses for broader tree island restoration efforts? Location: Loxahatchee Impoundment Landscape Assessment (LILA), Boynton Beach, Florida, USA. Methods: An experiment was designed to test hydrological and substrate effects on seedling growth and survivorship. Two islands – a peat and a limestone-core island representing two major types found in the Everglades – were constructed in four macrocosms. A mixture of eight tree species was planted on each island in March of 2006 and 2007. Survival and height growth of seedlings planted in 2006 were assessed periodically during the next two and a half years. Results: Survival and growth improved with increasing elevation on both tree island substrate types. Seedlings' survival and growth responses along a moisture gradient matched species distributions along natural hydrological gradients in the Everglades. The effect of substrate on seedling performance showed higher survival of most species on the limestone tree islands, and faster growth on their peat-based counterparts. Conclusions: The present results could have profound implications for restoration of forests on existing landforms and artificial creation of tree islands. Knowledge of species tolerance to flooding and responses to different edaphic conditions present in wetlands is important in selecting suitable species to plant on restored tree islands

Neuroendocrine control of a dynamic communication signal

Multiple physiological systems regulate the electric communication signal of the weakly electric gymnotiform fish, Brachyhypopomuspinnicaudatus. Fish were injected with neuroendocrine probes which identified pharmacologically relevant serotonin (5-HT) receptors similar to the mammalian 5-HT1AR and 5-HT2AR. Peptide hormones of the hypothalamic-pituitary-adrenal/interrenal axis also augment the electric waveform. These results indicate that the central serotonergic system interacts with the hypothalamic-pituitaryinterrenal system to regulate communication signals in this species. The same neuroendocrine probes were tested in females before and after introducing androgens to examine the relationship between sex steroid hormones, the serotonergic system, melanocortin peptides, and EOD modulations. Androgens caused an increase in female B. pinnicaudatus responsiveness to other pharmacological challenges, particularly to the melanocortin peptide adrenocorticotropic hormone (ACTH). A forced social challenge paradigm was administered to determine if androgens are responsible for controlling the signal modulations these fish exhibit when they encounter conspecifics. Males and females responded similarly to this social challenge construct, however introducing androgens caused implanted females to produce more exaggerated responses. These results confirm that androgens enhance an individual's capacity to produce an exaggerated response to challenge, however another unidentified factor appears to regulate sex-specific behaviors in this species. These results suggest that the rapid electric waveform modulations B. pinnicaudatus produces in response to conspecifics are situation-specific and controlled by activation of different serotonin receptor types and the subsequent effect on release of pituitary hormones.