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. ^

Three essays on the economics of defense contracting, output and income inequality

This dissertation analyzes both the economics of the defense contracting process and the impact of total dollar obligations on the economies of U.S. states. Using various econometric techniques, I will estimate relationships across individual contracts, state level output, and income inequality. I will achieve this primarily through the use of a dataset on individual contract obligations. ^ The first essay will catalog the distribution of contracts and isolate aspects of the process that contribute to contract dollar obligations. Accordingly, this study describes several characteristics about individual defense contracts, from 1966-2006: (i) the distribution of contract dollar obligations is extremely rightward skewed, (ii) contracts are unevenly distributed in a geographic sense across the United States, (iii) increased duration of a contract by 10 percent is associated with an increase in costs by 4 percent, (iv) competition does not seem to affect dollar obligations in a substantial way, (v) contract pre-payment financing increases the obligation of contracts from anywhere from 62 to 380 percent over non-financed contracts. ^ The second essay will turn to an aggregate focus, and look the impact of defense spending on state economic output. The analysis in chapter two attempts to estimate the state level fiscal multiplier, deploying Difference-in-Differences estimation as an attempt to filter out potential endogeneity bias. Interstate variation in procurement spending facilitates utilization of a natural experiment scenario, focusing on the spike in relative spending in 1982. The state level relative multiplier estimate here is 1.19, and captures the short run, impact effect of the 1982 spending spike. ^ Finally I will look at the relationship between defense contracting and income inequality. Military spending has typically been observed to have a negative relationship with income inequality. The third chapter examines the existence of this relationship, combining data on defense procurement with data on income inequality at the state level, in a longitudinal analysis across the United States. While the estimates do not suggest a significant relationship exists for the income share of the top ten percent of households, there is a significant positive relationship for the income share of top one percent households for an increase in defense procurement.^

Three Essays on the Economics of Defense Contracting, Output and Income Inequality

This dissertation analyzes both the economics of the defense contracting process and the impact of total dollar obligations on the economies of U.S. states. Using various econometric techniques, I will estimate relationships across individual contracts, state level output, and income inequality. I will achieve this primarily through the use of a dataset on individual contract obligations. The first essay will catalog the distribution of contracts and isolate aspects of the process that contribute to contract dollar obligations. Accordingly, this study describes several characteristics about individual defense contracts, from 1966-2006: (i) the distribution of contract dollar obligations is extremely rightward skewed, (ii) contracts are unevenly distributed in a geographic sense across the United States, (iii) increased duration of a contract by 10 percent is associated with an increase in costs by 4 percent, (iv) competition does not seem to affect dollar obligations in a substantial way, (v) contract pre-payment financing increases the obligation of contracts from anywhere from 62 to 380 percent over non-financed contracts. The second essay will turn to an aggregate focus, and look the impact of defense spending on state economic output. The analysis in chapter two attempts to estimate the state level fiscal multiplier, deploying Difference-in-Differences estimation as an attempt to filter out potential endogeneity bias. Interstate variation in procurement spending facilitates utilization of a natural experiment scenario, focusing on the spike in relative spending in 1982. The state level relative multiplier estimate here is 1.19, and captures the short run, impact effect of the 1982 spending spike. Finally I will look at the relationship between defense contracting and income inequality. Military spending has typically been observed to have a negative relationship with income inequality. The third chapter examines the existence of this relationship, combining data on defense procurement with data on income inequality at the state level, in a longitudinal analysis across the United States. While the estimates do not suggest a significant relationship exists for the income share of the top ten percent of households, there is a significant positive relationship for the income share of top one percent households for an increase in defense procurement.