Some of the properties of the specific summation methods will be investigated, such as what type of divergent series a method can or cannot sum, if the insertion of zeros into a series does change the sum, and when different methods give the same sum for a series.

Thesis advisor: Zhijie Xiao / I have three chapters in my dissertation. The first chapter is about the estimation and inference for DSGE model; the second chapter is about testing financial contagion among stock markets, and in the last chapter, I propose a new econometrics method to forecast inflation interval. This first chapter studies proper inference and asymptotically accurate structural break tests for parameters in Dynamic Stochastic General Equilibrium (DSGE) models in a maximum likelihood framework. Two empirically relevant issues may invalidate the conventional inference procedures and structural break tests for parameters in DSGE models: (i) weak identification and (ii) moderate parameter instability. DSGE literatures focus on dealing with weak identification issue, but ignore the impact of moderate parameter instability. This paper contributes to the literature via considering the joint impact of two issues in DSGE framework. The main results are: in a weakly identified DSGE model, (i) moderate instability from weakly identified parameters would not affect the validity of standard inference procedures or structural break tests; (ii) however, if strongly identified parameters are featured with moderate time-variation, the asymptotic distributions of test statistics would deviate from standard ones and would no longer be nuisance parameter free, which renders standard inference procedures and structural break tests invalid and provides practitioners misleading inference results; (iii) as long as I concentrate out strongly identified parameters, the instability impact of them would disappear as the sample size goes to infinity, which recovers the power of conventional inference procedure and structural break tests for weakly identified parameters. To illustrate my results, I simulate and estimate a modified version of the Hansen (1985) Real Business Cycle model and find that my theoretical results provide reasonable guidance for finite sample inference of the parameters in the model. I show that confidence intervals that incorporate weak identification and moderate parameter instability reduce the biases of confidence intervals that ignore those effects. While I focus on DSGE models in this paper, all of my theoretical results could be applied to any linear dynamic models or nonlinear GMM models. The second chapter, regarding the asymmetric and leptokurtic behavior of financial data, we propose a new contagion test in the quantile regression framework that is robust to model misspecification. Unlike conventional correlation-based tests, the proposed quantile contagion test allows us to investigate the stock market contagion at various quantiles, not only at the mean. We show that the quantile contagion test can detect a contagion effect that is possibly ignored by correlation-based tests. A wide range of simulation studies show that the proposed test is superior to the correlation-based tests in terms of size and power. We compare our test with correlation-based tests using three real data sets: the 1994 Tequila crisis, the 1997 Asia crisis, and the 2001 Argentina crisis. Empirical results show substantial differences between two types of tests. In the third chapter, I use Quantile Bayesian Approach-- to do the interval forecast for inflation in the semi-parametric framework. This new method introduces Bayesian solution to the quantile framework for two reasons: 1. It enables us to get more efficient quantile estimates when the informative prior is used (He and Yang (2012)); 2. We use Markov Chain Monte Carlo (MCMC) algorithm to generate samples of the posterior distribution for unknown parameters and take the mean or mode as the estimates. This MCMC estimator takes advantage of numerical integration over the standard numerical differentiation based optimization, especially when the likelihood function is complicated and multi-modal. Simulation results find better interval forecasting performance of Quantile Bayesian Approach than commonly used parametric approach. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

by Man Ka Sing. / Bibliography: leaves 69-70 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

Yau Chun-Yip. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 64-65). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fractional Integration --- p.1 / Chapter 1.2 --- Fractionally Intergrated Autoregressive Moving-Average Models With Conditional Heteroscedasticity --- p.6 / Chapter 1.3 --- Empirical Likelihood --- p.8 / Chapter 2 --- Whittle Likelihood Estimation in Long-Memory Time Series --- p.13 / Chapter 2.1 --- Exact Gaussian Maximum likelihood Estimation --- p.13 / Chapter 2.2 --- Whittle's approximate MLE --- p.16 / Chapter 3 --- Empirical Likelihood For ARFIMA models --- p.20 / Chapter 4 --- Empirical Likelihood For ARFIMA-GARCH models --- p.40 / Chapter 4.1 --- Empirical likelihood for GARCH models --- p.40 / Chapter 4.2 --- Empirical likelihood for ARFIMA-GARCH models --- p.44 / Chapter 5 --- Simulation --- p.48 / Chapter 5.1 --- Test of independece for periodogram ordinates --- p.49 / Chapter 5.2 --- Confidence Region --- p.53 / Chapter 5.3 --- Coverage error of empirical likelihood confidence intervals --- p.57 / Chapter 6 --- Conclusions and Further Research --- p.62 / Reference --- p.64

Tam, Chik Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 66-67). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Problem of identifying d in ARIMA model --- p.1 / Chapter 1.2 --- Another Approach --- p.4 / Chapter 2 --- Polyvariogram approach --- p.8 / Chapter 2.1 --- Variogram --- p.8 / Chapter 2.2 --- Polyvariogram --- p.11 / Chapter 2.3 --- A testing procedure --- p.13 / Chapter 2.4 --- Testing with integrated white noise series --- p.14 / Chapter 3 --- Aggregate time series in ARIMA --- p.17 / Chapter 3.1 --- The preservation of unity in ARIMA model under aggregation --- p.17 / Chapter 3.1.1 --- "Aggregation model of ARIMA(0,1,0)" --- p.20 / Chapter 3.1.2 --- "Aggregation model of ARIMA(0,1,1)" --- p.23 / Chapter 3.1.3 --- "Aggregation model of ARIMA(1,1,0)" --- p.26 / Chapter 4 --- Aggregation effects on the power of the test --- p.33 / Chapter 4.1 --- "Testing integrated white noise ARIMA(0,1.0) under aggregation" --- p.35 / Chapter 4.1.1 --- Simulation scheme --- p.35 / Chapter 4.1.2 --- Result --- p.39 / Chapter 4.2 --- "Testing ARIMA(0,1,1) under aggregation" --- p.42 / Chapter 4.2.1 --- Simulation scheme --- p.42 / Chapter 4.2.2 --- Result --- p.45 / Chapter 4.3 --- "Testing ARIMA(1, 1,0) under aggregation" --- p.52 / Chapter 4.3.1 --- Simulation scheme --- p.53 / Chapter 4.3.2 --- Result --- p.56 / Chapter 5 --- Conclusions and Discussions --- p.64

My thesis deals with finding counterexamples to Lubin’s Conjecture. Lubin’s Conjecture states that for power series f, g with coefficients in Zp, and f invertible and non-torsion, g non-invertible, then if f ◦ g = g ◦ f , f , g are endomorphisms of a formal group over Zp. This conjecture connects formal power series over the ring of p-adic integers (Zp) to formal groups. In this paper I will explain the properties of Formal Groups, their endomorphisms and logarithms, and will illustrate some properties of power series over the rings Qp and Zp.

Thesis (Ph. D.)--Oregon State University, 1963. / Typescript. Includes bibliographical references (leaves 180-182). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Chicago, 1912. / "Estratto dal tomo XXXIX (1⁰ sem. 1915) dei Rendiconti del Circolo matematico di Palermo." Also available on the Internet.

The exponential model of Bloomfield (1973) is becoming increasingly important due to its recent applications to long memory time series. However, this model has received little consideration in the context of short memory time series. Furthermore, there has been very little attempt at using the EXP model as a model to analyze observed time series data. This dissertation research is largely focused on developing new methods to improve the utility and robustness of the EXP model. Specifically, a new nonparametric method of parameter estimation is developed using wavelets. The advantage of this method is that, for many spectra, the resulting parameter estimates are less susceptible to biases associated with methods of parameter estimation based directly on the raw periodogram. Additionally, several methods are developed for the validation of spectral models. These methods test the hypothesis that the estimated model provides a whitening transformation of the spectrum; this is equivalent to the time domain notion of producing a model whose residuals behave like the residuals of white noise. The results of simulation and real data analysis are presented to illustrate these methods.

ABSTRACT Fan cooling is a fairly mainstream and well-developed technology. Vibration may make users feel uncomfortable. Assembly system may produce different noises right after the adverse effect components were destroyed, such as computer crashed or vibration or fan structural damage subsequently affects their fan reliability. Therefore, small vibration resonance amplification can not be overlooked. The researcher applied a 40 * 40 * 48mm fan to solve the problem of resonant vibration. He found the similar results of the natural frequencies of the structure of the fan by experimental and finite element analysis. In order to improve the vibration resonance, he changed the structural of the fans. In different structural designs, the natural frequencies did not change a lot. The natural frequency switched from 3000Hz to 3200Hz. To avoid the resonant frequency of the assemble fan, the researcher changed the number of fan blades and simulated the flow field. Compared the data to the experimental results, the results of the analysis were reasonable. The results showed the performance of the assembly fan did not necessarily need more leaves. The leaf numbers were from 7 (Inlet Fan) & 4 (Outlet Fan) into 5 (Inlet Fan) & 4 (Outlet Fan). Operation speed was changed from 14500 rpm (Inlet & Outlet Fan) to 15500 rpm (Inlet Fan) &11600 rpm (Outlet Fan). Using the fluid flow analysis, he found the change of the leaf number and operation speed of the fan could effectively avoid the resonance frequency and reduce vibration. An impact analysis was also helped to verify the capacity of the anti-impact of the fan. The structure of the fan after the preliminary design has been shaped mostly. By only changing the structural design to avoid excitation of the resonant frequency is difficult to achieve the effective function. To ensure the product stability, it is necessary to deal with the inducing vibration of the fluid flow.