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You searched for +publisher:"North Carolina State University" +contributor:("Sastry Pantula, Committee Member"). Showing records 1 – 3 of 3 total matches.

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North Carolina State University

1. Zhang, Ying. Testing for Unit Roots in Seasonal Time Series with Long Period.

Degree: PhD, Statistics, 2009, North Carolina State University

Testing for seasonal unit roots has been discussed extensively in the literature. However, the test will be difficult if the time series has a long period, where the critical values for the test statistics are not available. We modify the seasonal unit roots test of Dickey, Hasza, and Fuller (1984) to investigate results for less typical, long period cases, and present some asymptotic normality properties. We also suggest an empirical adjustment to improve the normal approximation when the seasonal period is not sufficiently long. The basic idea is to use a double-index form for the seasonal time series with a long period, where d denotes the large lag number, so that the d "channels" will be independent for each i. By applying the Classical Central Limit Theorem for iid random variables, we can obtain the asymptotic result. The convergence is proved to be order independent with respect to m and d. An advantage of this technique is that one can make the adjustment and use a standard normal as a reference distribution instead of looking into the seasonal percentile tables when doing the seasonal unit roots test, no matter what kind of deterministic terms are included in the model as long as the number of the regressors is fixed. We also show that for an AR(p) model we still obtain the asymptotic normality of the unit root statistics. Advisors/Committee Members: Marcia Gumpertz, Committee Member (advisor), Peter Bloomfield, Committee Member (advisor), David Dickey, Committee Chair (advisor), Sastry Pantula, Committee Member (advisor).

Subjects/Keywords: long period; seasonal time series; unit roots test

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APA (6th Edition):

Zhang, Y. (2009). Testing for Unit Roots in Seasonal Time Series with Long Period. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4362

Chicago Manual of Style (16th Edition):

Zhang, Ying. “Testing for Unit Roots in Seasonal Time Series with Long Period.” 2009. Doctoral Dissertation, North Carolina State University. Accessed January 24, 2020. http://www.lib.ncsu.edu/resolver/1840.16/4362.

MLA Handbook (7th Edition):

Zhang, Ying. “Testing for Unit Roots in Seasonal Time Series with Long Period.” 2009. Web. 24 Jan 2020.

Vancouver:

Zhang Y. Testing for Unit Roots in Seasonal Time Series with Long Period. [Internet] [Doctoral dissertation]. North Carolina State University; 2009. [cited 2020 Jan 24]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4362.

Council of Science Editors:

Zhang Y. Testing for Unit Roots in Seasonal Time Series with Long Period. [Doctoral Dissertation]. North Carolina State University; 2009. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4362


North Carolina State University

2. Lu, Na. Statistical Issues in Coherent Risk Management.

Degree: PhD, Statistics, 2004, North Carolina State University

Measuring risk is a crucial aspect of the portfolio optimization problem in finance, and of capital adequacy assessment in risk management. Expected Shortfall (ES) has been proposed as a coherent risk measure, by contrast with Value-at-Risk (VaR) and the standard-deviation-type of measures. Based on a coherent risk measure, for instance ES, we can discuss a coherent capital allocation for the purpose of internal risk management and performance measure, if ES is used for economic capital held by financial firms as a cushion to absorb the unexpected losses. Properly allocating risk capital down to the business level is important for the purpose of risk management and portfolio performance measurement. Even if there is a doubt about the reason for allocating ES, instead of VaR, the statistical properties of the statistic, marginal ES, from the proposed coherent allocation rule, are still of interest, because it is exactly the sensitivity of the target portfolio's ES. The idea of a coherent capital allocation rule by using a cost sharing rule, the Aumann-Shapley value in game theory, proposed by Denault (2001), happens to result in the same formula as proposed by Tasche (2000), who independently develops the "suitable" allocation rule based on the discussion of risk-adjusted returns. The fact, that two aspects of the concerns are satisfied by the same allocation formula, brings two fields together in an integrated way, so that a systematic risk management in a banking system seems very promising. Fundamental statistical issues arise in several places in a coherent risk management system. Primary interests will be, and are always, in modeling the profit/loss (P/L) distributions. Statistical modeling is receiving more and more attention currently, as well as economic modeling. For our purpose, we place more emphasis on the estimation and inference of ES and allocation statistics (marginal contribution of ES) under different situations. We also modify the back-testing rules based on ES. We propose a collection of weighted test statistics aiming at detecting the underestimated ES. Asymptotic properties of the test statistics are offered. The power of the tests in the context of an exponential family and the local alternatives is provided and the optimal weighting scheme is discussed. Advisors/Committee Members: Albert S. "Pete" Kyle, Committee Member (advisor), Sastry Pantula, Committee Member (advisor), Peter Bloomfield, Committee Chair (advisor), John Seater, Committee Member (advisor), Marc Genton, Committee Member (advisor).

Subjects/Keywords: sensitivity of ES; capital allocation; Value-at-Risk; partial moment; elliptical family; back-testing; risk management; expected shortfall; exponential family; optimal weighting

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lu, N. (2004). Statistical Issues in Coherent Risk Management. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3385

Chicago Manual of Style (16th Edition):

Lu, Na. “Statistical Issues in Coherent Risk Management.” 2004. Doctoral Dissertation, North Carolina State University. Accessed January 24, 2020. http://www.lib.ncsu.edu/resolver/1840.16/3385.

MLA Handbook (7th Edition):

Lu, Na. “Statistical Issues in Coherent Risk Management.” 2004. Web. 24 Jan 2020.

Vancouver:

Lu N. Statistical Issues in Coherent Risk Management. [Internet] [Doctoral dissertation]. North Carolina State University; 2004. [cited 2020 Jan 24]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3385.

Council of Science Editors:

Lu N. Statistical Issues in Coherent Risk Management. [Doctoral Dissertation]. North Carolina State University; 2004. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3385


North Carolina State University

3. Ravindran, Palanikumar. Bayesian Analysis of Circular Data Using Wrapped Distributions.

Degree: PhD, Statistics, 2003, North Carolina State University

Circular data arise in a number of different areas such as geological, meteorological, biological and industrial sciences. We cannot use standard statistical techniques to model circular data, due to the circular geometry of the sample space. One of the common methods used to analyze such data is the wrapping approach. Using the wrapping approach, we assume that, by wrapping a probability distribution from the real line onto the circle, we obtain the probability distribution for circular data. This approach creates a vast class of probability distributions that are flexible to account for different features of circular data. However, the likelihood-based inference for such distributions can be very complicated and computationally intensive. The EM algorithm used to compute the MLE is feasible, but is computationally unsatisfactory. Instead, we use Markov Chain Monte Carlo (MCMC) methods with a data augmentation step, to overcome such computational difficulties. Given a probability distribution on the circle, we assume that the original distribution was distributed on the real line, and then wrapped onto the circle. If we can "unwrap" the distribution off the circle and obtain a distribution on the real line, then the standard statistical techniques for data on the real line can be used. Our proposed methods are flexible and computationally efficient to fit a wide class of wrapped distributions. Furthermore, we can easily compute the usual summary statistics. We present extensive simulation studies to validate the performance of our method. We apply our method to several real data sets and compare our results to parameter estimates available in the literature. We find that the Wrapped Double Exponential family produces robust parameter estimates with good frequentist coverage probability. We extend our method to the regression model. As an example, we analyze the association between ozone data and wind direction. A major contribution of this dissertation is to illustrate a technique to interpret the circular regression coefficients in terms of the linear regression model setup. Regression diagnostics can be developed after augmenting wrapping numbers to the circular data (refer Section 3.5). We extend our method to fit time-correlated data. We can compute other statistics such as circular autocorrelation functions and their standard errors very easily. We use the Wrapped Normal model to analyze the hourly wind directions, which is an example of the time series circular data. Advisors/Committee Members: Dr. John Monahan, Committee Member (advisor), Dr. Sastry Pantula, Committee Member (advisor), Dr. Peter Bloomfield, Committee Member (advisor), Dr. Sujit K. Ghosh, Committee Chair (advisor).

Subjects/Keywords: Bayesian; Circular Data; Wrapped Normal; time series; regression

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Ravindran, P. (2003). Bayesian Analysis of Circular Data Using Wrapped Distributions. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3022

Chicago Manual of Style (16th Edition):

Ravindran, Palanikumar. “Bayesian Analysis of Circular Data Using Wrapped Distributions.” 2003. Doctoral Dissertation, North Carolina State University. Accessed January 24, 2020. http://www.lib.ncsu.edu/resolver/1840.16/3022.

MLA Handbook (7th Edition):

Ravindran, Palanikumar. “Bayesian Analysis of Circular Data Using Wrapped Distributions.” 2003. Web. 24 Jan 2020.

Vancouver:

Ravindran P. Bayesian Analysis of Circular Data Using Wrapped Distributions. [Internet] [Doctoral dissertation]. North Carolina State University; 2003. [cited 2020 Jan 24]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3022.

Council of Science Editors:

Ravindran P. Bayesian Analysis of Circular Data Using Wrapped Distributions. [Doctoral Dissertation]. North Carolina State University; 2003. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3022

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