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Recently there has been a surge in interest in coupling ensemble-based data assimilation methods with variational methods (commonly referred to as 4DVar). Here we discuss a number of important differences between ensemble-based and variational methods that ought to be considered when attempting to fuse these methods. We note that the Best Linear Unbiased Estimate (BLUE) of the posterior mean over a data assimilation window can only be delivered by data assimilation schemes that utilise the 4-dimensional (4D) forecast covariance of a prior distribution of non-linear forecasts across the data assimilation window. An ensemble Kalman smoother (EnKS) may be viewed as a BLUE approximating data assimilation scheme. In contrast, we use the dual form of 4DVar to show that the most likely non-linear trajectory corresponding to the posterior mode across a data assimilation window can only be delivered by data assimilation schemes that create counterparts of the 4D prior forecast covariance using a tangent linear model. Since 4DVar schemes have the required structural framework to identify posterior modes, in contrast to the EnKS, they may be viewed as mode approximating data assimilation schemes. Hence, when aspects of the EnKS and 4DVar data assimilation schemes are blended together in a hybrid, one would like to be able to understand how such changes would affect the mode-or mean-finding abilities of the data assimilation schemes. This article helps build such understanding using a series of simple examples. We argue that this understanding has important implications to both the interpretation of the hybrid state estimates and to their design.

Graduation date: 1983

This work is concerned with the theoretical study and the implementation of algorithms for solving two particular types of nonlinear optimization problems, namely unconstrained and simple-bound constrained optimization problems. For unconstrained optimization, we develop a new algorithm which uses a filter technique and a trust-region method in order to enforce global convergence and to improve the efficiency of traditional approaches. We also analyze the effect of approximate first and second derivatives on the performance of the filter-trust-region algorithm. We next extend our algorithm to simple-bound constrained optimization problems by combining these ideas with a gradient-projection method. Numerical results follow the proposed methods and indicate that they are competitive with more classical trust-region algorithms.

Thesis (M.S.)--University of Kentucky, 2002. / Title from document title page. Document formatted into pages; contains viii, 66 p. : ill. Includes abstract. Includes bibliographical references (p. 64-65).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Newton; globalized; inexact Newton. Includes bibliographical references (p. 61).

Filter trading rule is a technical trading strategy that was very popular amongst practitioners and has been used a lot for testing market efficiency. It has been shown that the filter trading rule is mathematically equivalent to the CUSUM quality control test as both are based on change point detection theory via sequential probability ratio tests (SPRT). To study the operating characteristics of the filter trading rule, many results from the CUSUM literature can be applied. However, some interesting operating characteristics of a technical trading rule such as expected profit per day may not be relevant when put into a quality control setting. In this thesis, we derive formulae for computing these operating characteristics. It is well known that just like any other technical trading rule, the filter trading rule is not effective when the asset price follows a random walk. In this thesis, we studied the statistical properties and effectiveness of the filter trading rule under different asset price models including Markov regime switching model and conditional heteroskedasticity model. The properties of the filter trading rule considered include the waiting time for the first signal in filter trading, the duration of a long or a short cycle in filter trading, the profit return derived from a long or a short cycle and the unit time return of long term filter trading. Built on the above results, we consider the problem of optimizing the performance of a filter trading rule by choosing a suitable filter size. For filter trading rule under the conditional heteroskedasticity model, the change point detection methods lead to a new technical trading rule called generalized filter trading rule in this thesis. The generalized filter trading rule is shown to have a better performance over the ordinary filter trading rule when it is applied to the trading of the Hang Seng Index futures contract. Finally, we have applied the filter trading rule to intraday trading on high frequency Hang Seng Index futures data. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains vi, 77 p. Includes abstract. Includes bibliographical references (p. 75-77). WVU users: Also available in print for a fee.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographical references (p. 49.