博士（経済学） / 甲第99号 / 155p / Hitotsubashi University

Due essentially to the difficulties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to specific skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found. While conventional time series analysis greatly depends on the assumption of stationarity, measurements taken from many physical systems, which consist of both periodicity and randomness, often exhibit cyclostationarity (i.e., a periodic structure in their first- and second-order moments). Identifying the hourly global horizontal irradiances (GHIs), collected at a solar monitoring station of Saudi Arabia, as a cyclostationary process and considering the significant impact of that on the energy production in Saudi Arabia, Chapter 3 provides a temporal model of GHIs. Chapter 4 extends the analysis to a spatio-temporal cyclostationary modeling of 45 different solar monitoring stations of the Kingdom. Both the proposed models are shown to produce better forecasts, more realistic simulations, and reliable photovoltaic power estimates in comparison to a classical model that fails to recognize the GHI data as cyclostationary. Chapter 5 extends the notion of cyclostationarity to a novel and flexible class of processes, coined evolving period and amplitude cyclostationary (EPACS) processes, that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using a simulation study and a real data example, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae. Finally, Chapter 6 summarizes the findings of the thesis and discusses its significance and possible future extensions.

No description available.

Dauphin, Petit Bois, and Horn Island form the Alabama gulf-barrier chain directly south of Mobile Bay. Many studies have targeted local climate stressors and the flux of longshore currents as factors for erosional and accretional changes on these islands, but little attention is paid to the degradation of their vegetative dune-systems as a contributor to their shoreline morphology (Hanley et al., 2014; Smith, 2018; Byrnes, 2010). This study fills this literary gap, utilizing GIS raster classification and Digital Shoreline Analysis System to measure vegetative health and shoreline change on these islands and verify a relationship between these two factors. The distribution of vegetation on the Barrier Islands has been shown to mitigate shoreline changes, particularly ocean-side erosion. This thesis has significance in that it geo-statistically verified the importance of natural infrastructure, vegetative dune systems, in shoreline stability using GIS.

No description available.

The stability of the spine can be estimated from kinematic variability and nonlinear analyses of seated balance tasks. However, processing methods require sufficient signal duration and test-retest experiments require that the assessment must be reliable. Our goal was to characterize the reliability and establish the trial duration for spine stability assessment. Stationarity, kinematic variability and nonlinear dynamic stability were quantified from kinetic and kinematic data collected during balance performance. Stationarity results showed that a minimum 30 seconds test duration is necessary. Intra-session reliability was excellent, however inter-session reliability needed more test trials to achieve excellent reliability. Few studies have investigated the spinal stability during pushing and pulling exertions. Past studies suggest that the spine can be stabilized by paraspinal muscle stiffness as well as reflexes. We hypothesized that the stability of the spine decreases with exertion force and decreases during pushing more than during pulling exertion. Kinematic variability and nonlinear dynamic stability measurements were quantified from the balance performance during isometric pushing and pulling tasks. Results demonstrated that spinal stability decreased with exertion force and decreased a greater amount during pushing task than during pulling task. Stiffness alone may be insufficient to stabilize the trunk. Results may be able to be explained by slower reflex delay. The results suggested that pushing and pulling exertions have a potential risk of low-back disorders. / Master of Science

No / We study the price and liquidity effects following the FTSE 100 index revisions. We employ the standard GARCH(1,1) model to allow the residual variance of the single index model (SIM) to vary systematically over time and use a Kalman filter approach to model SIM coefficients as a random walk process. We show that the observed price effect depends on the abnormal return estimation methods. Specifically, the OLS-based abnormal returns indicate that the price effect associated with the index revision is temporary, whereas both SIM with random coefficients and GARCH(1,1) model suggest that both additions and deletions experience permanent price change. Added (removed) stocks exhibit permanent (temporary) change in trading volume and bid-ask spread. The analysis of the spread components suggests that the permanent change associated with additions is a result of non-information-related liquidity. We interpret the permanent price effect of additions and deletions combined with the permanent (temporary) shift in liquidity of added (removed) stocks as evidence in favour of the imperfect substitution hypothesis with some non-information-related liquidity effects in the case of additions.

This thesis is interested in describing stationary random discrete signals, especially) in music discrete signals. Here is described when is signal stationary and when is not stationary. It contains tip for preprocessing of signal for accurate recognition of local stationarity. Thesis contain mathematical definition of parameters of random digital signals, which are used for stationarity recognition. It is followed by description of basic windows, their categories, describing of their parameters and comparing of each. In next part of thesis are described mothods of segmentations with constant window constant overlap save, constant window constant ovelap add, variable window constant overlap save, variable window constant ovelap add and variable window variable overlap add. It is followed by analyzing of windows used in segmentations with variable lengths of segments. As next point of thesis are transients made by step changes of coefficients of filter in filtering of segments with variable lengths. At the end is investigated the best accurate method of signal stationarity detection. Segments made by accurate method of detection are analyzed. thesis contains exapmle of music signal segmentation.

Simplifications regarding calculations of fatigue life due to vibrational loading is based on weakly stationarity assumptions which is a time independent method. The hypothesis was based on the uncertainty of these assumptions. The aim of this study was to examine whether the analysed data fulfilled the assumptions of weakly stationarity. It was determined that the assumption was not valid for most signals and a comparison of time dependent methods should be performed to evaluate the difference compared with the time independent method. Two time dependent methods were constructed and implemented on the signals based on the results of performed stationarity tests. The result determined that a decrease in fatigue life of an investigated weld might occur for the two time dependent methods compared with the time independent method. The method which was considered to produce the most accurate results was also the most constrained as to the amount of data that fulfilled its requirements. A conclusion was drawn that signals containing more data was necessary to achieve conclusive results of the fatigue life. The hypothesis was proven to be mostly true since most of the analysed signals were found to be piecewise weakly stationary.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Turbulent flow high complexity makes it difficult to describe complex phenomena, such as the transport of vector and scalar quantities at the lower atmosphere, making the analysis of experimental data, such as time series, largely employed. The method mostly used by the micrometeorological community to quantify such turbulent transport is associated with the determination of the statistical covariance between two variables. It is known that the determination of statistical quantities for very long temporal windows leads to a large flux uncertainty. At the same time, the theory indicates that the association between fluxes and statistical covariance is only valid for temporally stationary series. The aim of the present study is to test the hypothesis that the estimate uncertainty is directly related to the series non-stationarity. To better understand this issue, we use a methodology based on a group of parametric and nonparametric statistical tests. The tests considered here are the T-test, F-test, median test, U-test and run test. Furthermore, the test results are compared with the outputs of two signal decomposition procedures: multiresolution analysis and empirical mode decomposition. The results suggest that the flux variability over large temporal scales characterizes the existence of temporal trends and low frequency components in the time series considered, so that it is more associated with an observational limitation of the analysis than with non-stationarity, as this concept should be the property of an ensemble, rather than of a single realization. Such limitation suggests the definition of a practical single order stationarity, associated with temporal trends and low frequency components whose energy is similar or larger to that of the turbulent fluctuations. For that reason, we affirm that the interactions test is, among all considered, the best suited for analyzing atmospheric data, because it is the most sensible to the existence of temporal trends. Furthermore, such test allows obtaining a temporal scale beyond which mesoscale events become important. / A complexidade de escoamentos turbulentos causa dificuldade para a descrição de fenômenos complexos, como o transporte de grandezas vetoriais e escalares na baixa atmosfera, fazendo com que a análise de dados experimentais, principalmente séries temporais, seja amplamente utilizada. O método mais utilizado pela comunidade micrometeorológica para quantificar esse transporte pela turbulência está associado à determinação da covariância entre duas variáveis. Sabe-se que a determinação de quantidades estatísticas para janelas temporais muito longas resulta em uma grande incerteza nos valores dos fluxos obtidos através desse método. Ao mesmo tempo, a teoria indica que o procedimento de associar fluxos a covariâncias estatísticas só vale para séries temporalmente estacionárias. O objetivo deste trabalho é testar a hipótese de que a incerteza das estimativas esteja relacionada diretamente com a não-estacionariedade das séries temporais. Para entendermos melhor isso, usamos uma metodologia baseada em um conjunto de testes estatísticos paramétricos e não-paramétricos de hipótese nula. Os testes considerados são o teste-T, teste-F, teste da mediana, teste-U e o teste das interações. Os resultados dos testes são ainda comparados com os obtidos com dois métodos de decomposição de sinais: a análise de multiresolução e a Decomposição Empírica de Modos. Os resultados sugerem que a variabilidade dos fluxos nas grandes escalas temporais está associada diretamente com a presença de tendências e componentes de baixa frequência nas séries analisadas, e que este fato está mais ligado à limitação observacional em que a análise é realizada do que propriamente com a não-estacionariedade, já que esta última é uma propriedade de ensemble e não de apenas uma realização. Esta limitação sugere a definição de um conceito mais prático de estacionariedade de primeira ordem, que seja associado à presença de tendências ou componentes de baixa frequência com energias da ordem ou maiores que a energia das escalas turbulentas. Por esse motivo podemos afirmar que na análise de dados atmosféricos o teste das interações mostrou-se, entre todos os considerados, o mais sensível à presença de tendências, permitindo inclusive a obtenção de uma escala temporal na qual os eventos de meso/submesoescala ganham importância.