A major objective of this thesis is to study the statistical inference problem for GARCH-type models, including fractionally-integrated (FI) GARCH, fractional (F) GARCH, long-memory (LM) GARCH, and non-stationary GARCH models. / Among various types of generalizations to the ARCH models, fractionally-integrated (FI) GARCH model proposed in Baillie et al. (1996) and Bollerslev and Mikkelson (1996) is one of the most interesting ones as it offered many challenging theretical problems. / Parameters in the ARCH-type models are commonly estimated using the quasi-maximum likelihood estimator (QMLE). To establish consistency and asymptotic normality of the QMLE, one usually has to impose stringent assumptions, see Robinson and Zaffaroni (2006) and Straumann (2005). They have to assume that a stationary solution to the true model exists and this solution has some finite moments. These two assumptions are too restrictive to be applied to FIGARCH models. Formal results of the asymptotic properties of the QMLE of the FIGARCH models are still not available. Progresses on asymptotic theory of QMLE have only been made on certain models that resemble the FIGARCH model, including the FGARCH model of Ding and Granger (1996) and Robinson and Zaffaroni (2006), the LM-GARCH model of Robinson and Zaffaroni (1997) and the non-stationary ARCH model, but not the FIGARCH model itself. / This study attempts to solve the FIGARCH problem and extend the current findings on FGARCH, LM-GARCH and non-stationary GARCH models. We show that if the fractional parameter d is known, the QMLE for the parameters are strongly consistent and asymptotically normal. The results of LM-GARCH (0, d, 0) model in Konlikov (2003a,b) will be generalized to encompass the LM-GARCH(p, d, q) models. We also furnish a general result for non-stationary GARCH (p, q) models, extending the results of Jensen and Rahbek (2004) on weak consistency and asymptotic normality of the QMLE of the non-stationary GARCH (1, 1) models. / Ng, Chi Tim. / "June 2007." / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Ho, Sin Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 49-52). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Autoregressive moving average time series --- p.1 / Chapter 1.2 --- Integrated stationary time series --- p.3 / Chapter 1.3 --- Some existing methods of identifying d --- p.4 / Chapter 1.4 --- Introduction to Cressie's --- p.6 / Chapter 1.5 --- Outline of thesis --- p.6 / Chapter 2 --- Variogram and Polyvariogram --- p.7 / Chapter 2.1 --- Introduction to variogram --- p.7 / Chapter 2.2 --- Polyvariogram of order b --- p.8 / Chapter 3 --- Testing Procedure --- p.10 / Chapter 3.1 --- Testing for an integrated white noise series --- p.10 / Chapter 3.2 --- Testing for an integrated ARM A series --- p.11 / Chapter 3.3 --- Testing for an integrated linear process --- p.12 / Chapter 4 --- Simulation Results --- p.14 / Chapter 4.1 --- Choice of series length n and r --- p.14 / Chapter 4.2 --- Integrated ARMA series --- p.21 / Chapter 4.3 --- Integrated linear process --- p.39 / Chapter 4.4 --- Comparisons with some methods in literatures --- p.43 / Chapter 4.5 --- An illustrative example --- p.45 / Chapter 5 --- Concluding Remark --- p.48 / Bibliography --- p.49

Zhou, Tu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 61-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.0 / Chapter 1.1 --- Motivation and Objective --- p.0 / Chapter 1.2 --- Major Contribution --- p.2 / Chapter 1.3 --- Thesis Organization --- p.4 / Chapter 2 --- Measurement of Relationship between financial time series --- p.5 / Chapter ´ب2.1 --- Linear Correlation --- p.5 / Chapter 2.1.1 --- Pearson Correlation Coefficient --- p.6 / Chapter 2.1.2 --- Rank Correlation --- p.6 / Chapter 2.2 --- Mutual Information --- p.7 / Chapter 2.2.1 --- Approaches of Mutual Information Estimation --- p.10 / Chapter 2.3 --- Copula --- p.12 / Chapter 2.4 --- Analysis from Experimental Data --- p.14 / Chapter 2.4.1 --- Experiment 1: Nonlinearity --- p.14 / Chapter 2.4.2 --- Experiment 2: Sensitivity of Outliers --- p.16 / Chapter 2.4.3 --- Experiment 3: Transformation Invariance --- p.20 / Chapter 2.5 --- Chapter Summary --- p.23 / Chapter 3 --- Clustered Dynamic Conditional Correlation Model --- p.26 / Chapter 3.1 --- Background Review --- p.26 / Chapter 3.1.1 --- GARCH Model --- p.26 / Chapter 3.1.2 --- Multivariate GARCH model --- p.29 / Chapter 3.2 --- DCC Multivariate GARCH Models --- p.31 / Chapter 3.2.1 --- DCC GARCH Model --- p.31 / Chapter 3.2.2 --- Generalized DCC GARCH Model --- p.32 / Chapter 3.2.3 --- Block-DCC GARCH Model --- p.32 / Chapter 3.3 --- Clustered DCC GARCH Model --- p.34 / Chapter 3.3.1 --- Minimum Distance Estimation (MDE) --- p.36 / Chapter 3.3.2 --- Clustered DCC (CDCC) based on MDE --- p.37 / Chapter 3.4 --- Clustering Method Selection --- p.40 / Chapter 3.5 --- Model Estimation and Testing Method --- p.42 / Chapter 3.5.1 --- Maximum Likelihood Estimation --- p.42 / Chapter 3.5.2 --- Box-Pierce Statistic Test --- p.44 / Chapter 3.6 --- Chapter Summary --- p.44 / Chapter 4 --- Experimental Result and Applications on CDCC --- p.46 / Chapter 4.1 --- Model Comparison and Analysis --- p.46 / Chapter 4.2 --- Portfolio Selection Application --- p.50 / Chapter 4.3 --- Value at Risk Application --- p.52 / Chapter 4.4 --- Chapter Summary --- p.55 / Chapter 5 --- Conclusion --- p.57 / Bibliography --- p.61

This thesis examines the relations among emotions and musical features and their changes with time, based on the assertion that there exist underlying, culturally specific, quantifiable rules which govern these relations. I designed, programmed and tested a computer controlled Two-Dimensional Emotion Space (2DES) which administered and controlled all aspects of the experimental work. The 2DES instrument consisted of two bipolar emotional response (ER) dimensions: valence (happiness-sadness) and arousal (activeness-sleepiness). The instrument had a test-retest reliability exceeding 0.83 (p &gt 0.01, N = 28) when words and pictures of facial expressions were used as the test stimuli. Construct validity was quantified (r &lt 0.84, p &gt 0.01). The 2DES was developed to collect continuous responses to recordings of four movements of music (N = 67) chosen to elicit responses in all quadrants of the 2DES: &quotMorning&quot from Peer Gynt, Adagio from Rodrigo???s Concierto de Aranjuez (Aranjuez), Dvorak???s Slavonic Dance Op 42, No. 1 and Pizzicato Polka by Strauss. Test-retest reliability was 0.74 (p &gt 0.001, N = 14). Five salient and objectively quantifiable features of the musical signal (MFs) were scaled and used for time series analysis of the stimuli: melodic pitch, tempo, loudness, frequency spectrum centroid (timbral sharpness) and texture (number of different instruments playing). A quantitative analysis consisted of: (1) first order differencing to remove trends, (2) determination of suitable, lagged MFs to keep as regressors via stepwise regression, and (3) regression of each ER onto selected MFs with first order autoregressive adjustment for serial correlation. Regression coefficients indicated that first order differenced (???) loudness and ???tempo had the largest correlations with ???arousal across all pieces, and ???melodic pitch correlated with ???valence for Aranjuez (p &gt 0.01 for all coefficients). The models were able to explain up to 73% of mean response variance. Additional variation was explained qualitatively as being due to interruptions, interactions and collinearity: The minor key and dissonances in a tonal context moved valence toward the negative direction; Short duration and perfect cadences moved valence in the positive direction. The 2DES measure and serial correlation adjusted regression models were, together, shown to be powerful tools for understanding relations among musical features and emotional response.

Amar G. Bose. / "May 15, 1956." "This report is based on a thesis submitted to the Department of Electrical Engineering, M.I.T., May 14, 1956, in partial fulfillment of the requirements for the degree of Doctor of Science." / Bibliography: p. 58. / Army Signal Corps Contract DA36-039-sc-64637 Dept. of the Army Task No. 3-99-06-108 Project No. 3-99-00-100

John P. Costas. / "May 16, 1950." / Bibliography: p. 7. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B Dept. of the Army Project No. 3-99-10-022

Time series analysis of Synthetic Aperture Radar Interferometry (InSAR) data has become an important scientific tool for monitoring and measuring the displacement of Earth’s surface due to a wide range of phenomena, including earthquakes, volcanoes,landslides, changes in ground water levels, and wetlands. Time series analysis is a product of interferometric phase measurements, which become ambiguous when the observed motion is larger than half of the radar wavelength. Thus, phase observations must first be unwrapped in order to obtain physically meaningful results. Persistent Scatterer Interferometry (PSI), Stanford Method for Persistent Scatterers (StaMPS), Short Baselines Interferometry (SBAS) and Small Temporal Baseline Subset (STBAS)algorithms solve for this ambiguity using a series of spatio-temporal unwrapping algorithms and filters. In this dissertation, I improve upon current phase unwrapping algorithms, and apply the PSI method to study subsidence in Mexico City. PSI was used to obtain unwrapped deformation rates in Mexico City (Chapter 3),where ground water withdrawal in excess of natural recharge causes subsurface, clay-rich sediments to compact. This study is based on 23 satellite SAR scenes acquired between January 2004 and July 2006. Time series analysis of the data reveals a maximum line-of-sight subsidence rate of 300mm/yr at a high enough resolution that individual subsidence rates for large buildings can be determined. Differential motion and related structural damage along an elevated metro rail was evident from the results. Comparison of PSI subsidence rates with data from permanent GPS stations indicate root mean square(RMS) agreement of 6.9 mm/yr, about the level expected based on joint data uncertainty.The Mexico City results suggest negligible recharge, implying continuing degradation and loss of the aquifer in the third largest metropolitan area in the world. Chapters 4 and 5 illustrate the link between time series analysis and three-dimensional (3-D) phase unwrapping. Chapter 4 focuses on the unwrapping path.Unwrapping algorithms can be divided into two groups, path-dependent and path-independent algorithms. Path-dependent algorithms use local unwrapping functions applied pixel-by-pixel to the dataset. In contrast, path-independent algorithms use global optimization methods such as least squares, and return a unique solution. However, when aliasing and noise are present, path-independent algorithms can underestimate the signal in some areas due to global fitting criteria. Path-dependent algorithms do not underestimate the signal, but, as the name implies, the unwrapping path can affect the result. Comparison between existing path algorithms and a newly developed algorithm based on Fisher information theory was conducted. Results indicate that Fisher information theory does indeed produce lower misfit results for most tested cases. Chapter 5 presents a new time series analysis method based on 3-D unwrapping of SAR data using extended Kalman filters. Existing methods for time series generation using InSAR data employ special filters to combine two-dimensional (2-D) spatial unwrapping with one-dimensional (1-D) temporal unwrapping results. The new method,however, combines observations in azimuth, range and time for repeat pass interferometry. Due to the pixel-by-pixel characteristic of the filter, the unwrapping path is selected based on a quality map. This unwrapping algorithm is the first application of extended Kalman filters to the 3-D unwrapping problem. Time series analyses of InSAR data are used in a variety of applications with different characteristics. Consequently, it is difficult to develop a single algorithm that can provide optimal results in all cases, given that different algorithms possess a unique set of strengths and weaknesses. Nonetheless, filter-based unwrapping algorithms such as the one presented in this dissertation have the capability of joining multiple observations into a uniform solution, which is becoming an important feature with continuously growing datasets.

Thesis (M. Phil.)--University of Hong Kong, 2006. / Also available in print.

Ph.D. / Electrical and Computer Engineering / Numerous applications require either the estimation or prediction of a noisy time-series. Examples include speech enhancement, economic forecasting, and geophysical modeling. A noisy time-series can be described in terms of a probabilistic model, which accounts for both the deterministic and stochastic components of the dynamics. Such a model can be used with a Kalman filter (or extended Kalman filter) to estimate and predict the time-series from noisy measurements. When the model is unknown, it must be estimated as well; dual estimation refers to the problem of estimating both the time-series, and its underlying probabilistic model, from noisy data. The majority of dual estimation techniques in the literature are for signals described by linear models, and many are restricted to off-line application domains. Using a probabilistic approach to dual estimation, this work unifies many of the approaches in the literature within a common theoretical and algorithmic framework, and extends their capabilities to include sequential dual estimation of both linear and nonlinear signals. The dual Kalman filtering method is developed as a method for minimizing a variety of dual estimation cost functions, and is shown to be an effective general method for estimating the signal, model parameters, and noise variances in both on-line and off-line environments.