Στο πρώτο κεφάλαιο εισάγουμε τις βασικές έννοιες της διπλωματικής εργασίας. Αναφέρουμε τους ορισμούς και τον σκοπό της ανάλυσης χρονολογικών σειρών. Επίσης εισάγονται ορισμένα βασικά χαρακτηριστικά των χρονολογικών σειρών όπως η έννοια της στασιμότητας και της συνάρτησης αυτοσυσχέτισης και αναφέρουμε τις τρεις βασικές κατηγορίες στοχαστικών υποδειγμάτων χρονολογικών σειρών που αφορούν στις στάσιμες στοχαστικές διαδικασίες, οι οποίες θα αναλυθούν στα επόμενα κεφάλαια. Στο δεύτερο κεφάλαιο αναλύουμε τα αυτοπαλίνδρομα υποδείγματα, πρώτης, δεύτερης και γενικά p τάξης. Αναφέρονται παραδείγματα. Στο τρίτο κεφάλαιο αναλύουμε τα υποδείγματα κινητού μέσου πρώτης και γενικά q τάξης καθώς και μεικτά υποδείγματα πρώτης και γενικά (p,q) τάξης. Αναφέρονται παραδείγματα. Στο τέταρτο κεφάλαιο αναλύουμε χρονολογικές σειρές που δεν έχουν τα χαρακτηριστικά στάσιμων στοχαστικών διαδικασιών. Επίσης αναλύουμε την μεθοδολογία Box-Jenkins, η οποία είναι μία μέθοδος εξεύρεσης ενός στατιστικού υποδείγματος (ARIMA). Τέλος εφαρμόζεται η παραπάνω μέθοδος σε ένα παράδειγμα με τη χρήση του SPSS. / At the first chapter we introduce the basic concepts. We present the main definitions and the objectives of the time series analysis. Furthermore, we introduce some basic characteristics of the time series such as the concepts of “stationary process” and “autocorrelation”. Finally we mention three basic categories of time series models that concern stationary stochastic processes. Following in the second chapter we analyze the autoregressive models of first, second and generally “p” order. We present various relative examples. At the third chapter we analyze the moving average models of first and generally “q” order. Additionally, we analyze the mixed models of first and generally (p,q) order. Various relative examples are presented. Finally, at the forth chapter we analyze time series that don’t have the characteristics of stationary stochastic proceedings. Also we analyze the method Box-Jenkins. Furthermore, the later method is studied using the statistic software package SPSS.

Master of Science / Department of Statistics / Juan Du / Space and time are often vital components of research data sets. Accounting for and utilizing the space and time information in statistical models become beneficial when the response variable in question is proved to have a space and time dependence. This work focuses on the modeling and analysis of crop yield over space and time. Specifically, two different yield data sets were used. The first yield and environmental data set was collected across selected counties in Kansas from yield performance tests conducted for multiple years. The second yield data set was a survey data set collected by USDA across the US from 1900-2009. The objectives of our study were to investigate crop yield trends in space and time, quantify the variability in yield explained by genetics and space-time (environment) factors, and study how spatio-temporal information could be incorporated and also utilized in modeling and forecasting yield. Based on the format of these data sets, trend of irrigated and dryland crops was analyzed by employing time series statistical techniques. Some traditional linear regressions and smoothing techniques are first used to obtain the yield function. These models were then improved by incorporating time and space information either as explanatory variables or as auto- or cross- correlations adjusted in the residual covariance structures. In addition, a multivariate time series modeling approach was conducted to demonstrate how the space and time correlation information can be utilized to model and forecast yield and related variables. The conclusion from this research clearly emphasizes the importance of space and time components of data sets in research analysis. That is partly because they can often adjust (make up) for those underlying variables and factor effects that are not measured or not well understood.

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / Feher Keying (FK) signals are clock shaped baseband waveforms with the potential to attain very high spectral efficiencies. Two FK signals which have different level rectangular waveforms (named as FK-1) or sinusoidal waveforms (named as FK-2) for two binary symbols are considered in this paper. These signals have periodic components in the time domain. Therefore they have cyclostationary properties. This means that spectral correlation exists in the frequency domain. For each type of waveforms, spectral correlation has been investigated. FK signals can be expressed mathematically into two parts in the frequency domain – discrete part and continuous part. The discrete part has one or more discrete impulse(s) in their spectra and the continuous part has periodically the same shape of harmonics in their spectra. The correlations of their spectra have been obtained mathematically and by simulation. It is shown that FK signals have high correlation related to the symbol rate. Finally, some suggestions how these properties can be used to improve their performance by devising better demodulators are discussed. These properties can be used for interference rejection at the receiver, which results in low bit error rate performance.

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random" yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. One important type of pseudorandom sequences is the sequences generated by feedback with carry shift registers (FCSRs). In this dissertation, we study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2. These are called half-ℓ-sequences. More precisely, our work includes: The number of occurrences of one symbol within one period of a half-ℓ-sequence; The number of pairs of symbols with a fixed distance between them within one period of a half-ℓ-sequence; The number of triples of consecutive symbols within one period of a half-ℓ-sequence. In particular we give a bound on the number of occurrences of one symbol within one period of a binary half-ℓ-sequence and also the autocorrelation value in binary case. The results show that the distributions of half-ℓ-sequences are fairly flat. However, these sequences in the binary case also have some undesirable features as high autocorrelation values. We give bounds on the number of occurrences of two symbols with a fixed distance between them in an ℓ-sequence, whose period reaches the maximum and obtain conditions on the connection integer that guarantee the distribution is highly uniform. In another study of a cryptographically important statistical property, we study a generalization of correlation immunity (CI). CI is a measure of resistance to Siegenthaler's divide and conquer attack on nonlinear combiners. In this dissertation, we present results on correlation immune functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, to measure the proximity of two functions. We give two definitions of q-correlation immune functions and the relationship between them. Certain properties and constructions for q-correlation immune functions are discussed. We examine the connection between correlation immune functions and q-correlation immune functions.

Spatial interaction models of the gravity type are widely used to model origindestination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterise an origin region of a flow, variables that characterise a destination region of a flow, and finally variables that measure the separation between origin and destination regions. This paper outlines and compares two approaches, the spatial econometric and the eigenfunction-based spatial filtering approach, to deal with the issue of spatial autocorrelation among flow residuals. An example using patent citation data that capture knowledge flows across 112 European regions serves to illustrate the application and the comparison of the two approaches.(authors' abstract)

In many events affecting our civil infrastructure, such as contamination or weathering, it is likely that only the surfaces of the affected building materials will be available for non-destructive measurements. In this work, we describe and analyze surface gas permeability measurements on a variety of natural and engineered building materials using two types of relatively new, non-destructive surface permeameters. It is shown that the surface gas permeability measurements correlate well with each other and could provide rapid estimates of macroscopic gas permeability and degradation of materials due to weathering. It is hypothesized that surface permeability can be used to predict macroscopic wicking of water. The results indicated that macroscopic wicking correlated reasonably well with surface permeability measurements of uniform materials with low permeabilities such as sandstones and clay brick.

Digitized acoustical signals of Byzantine music performed by Iakovos Nafpliotis are used to extract the fundamental frequency of each note of the diatonic scale. These empirical results are then contrasted to the theoretical suggestions and previous empirical findings. Several parametric and non-parametric spectral parameter estimation methods are implemented. These include: (1) Phase vocoder method, (2) McAulay-Quatieri method, (3) Levinson-Durbin algorithm,(4) YIN, (5) Quinn & Fernandes Estimator, (6) Pisarenko Frequency Estimator, (7) MUltiple SIgnal Characterization (MUSIC) algorithm, (8) Periodogram method, (9) Quinn & Fernandes Filtered Periodogram, (10) Rife & Vincent Estimator, and (11) the Fourier transform. Algorithm performance was very precise. The psychophysical aspect of human pitch discrimination is explored. The results of eight (8) psychoacoustical experiments were used to determine the aural just noticeable difference (jnd) in pitch and deduce patterns utilized to customize acceptable performable pitch deviation to the application at hand. These customizations [Acceptable Performance Difference (a new measure of frequency differential acceptability), Perceptual Confidence Intervals (a new concept of confidence intervals based on psychophysical experiment rather than statistics of performance data), and one based purely on music-theoretical asymphony] are proposed, discussed, and used in interpretation of results. The results suggest that Nafpliotis' intervals are closer to just intonation than Byzantine theory (with minor exceptions), something not generally found in Thrasivoulos Stanitsas' data. Nafpliotis' perfect fifth is identical to the just intonation, even though he overstretches his octaveby fifteen (15)cents. His perfect fourth is also more just, as opposed to Stanitsas' fourth which is directionally opposite. Stanitsas' tendency to exaggerate the major third interval A4-F4 is still seen in Nafpliotis, but curbed. This is the only noteworthy departure from just intonation, with Nafpliotis being exactly Chrysanthian (the most exaggerated theoretical suggestion of all) and Stanitsas overstretching it even more than Nafpliotis and Chrysanth. Nafpliotis ascends in the second tetrachord more robustly diatonically than Stanitsas. The results are reported and interpreted within the framework of Acceptable Performance Differences.

Orientadora: Marcela Aparecida Guerreiro Machado / Coorientador: Antonio Fernando Branco Costa / Banca: Fernando Augusto Silva Marins / Banca: Aneirson Francisco da Silva / Banca: José Luiz Contador / Banca: Bruno Chaves Franco / Resumo: A suposição mais importante para o emprego dos gráficos de controle é a de independência entre as medidas da característica de qualidade de um processo. A violação da hipótese de independência diminui o poder de detecção do gráfico de controle. Nesta tese, o gráfico ����2 de Hotelling é empregado para monitorar processos bivariados com observações da amostra representadas por um modelo autoregressivo multivariado de primeira ordem - VAR(1). Contrapondo a esse efeito negativo da falta de independência, são sugeridas duas estratégias de amostragem: (1) na estratégia de amostragem sistemática, as amostras são obtidas através da seleção de um elemento da linha de produção e, em seguida, pulam-se s elementos consecutivos antes de se selecionar o próximo; (2) na estratégia de amostragem composta, os elementos são selecionados de dois subgrupos racionais consecutivos para formar a amostra. O emprego dessas estratégias sempre melhoram o desempenho do gráfico, exceto quando apenas uma variável é afetada por uma causa especial e as observações desta variável não são autocorrelacionadas. Os ensaios realizados mostraram que se pular s=1 elemento com a estratégia sistemática, o número médio de amostras até o sinal (NMA) reduz em mais de 30%, em média. Se dois itens são pulados (s=2), esse número aumenta para 40%. Na estratégia de amostragem composta, observou-se uma redução média de 25% no NMA / Abstract: The most important of the assumptions made concerning control charts is that of independence of the quality characteristics observations. The violation of the independence assumption decreases the power of the control chart. In this thesis, is considered the T2 control chart for bivariate samples of size n with observations modeled by a first order vector autoregressive model - VAR (1). To counteract the undesired effect of the autocorrelation two sampling strategies are applied: (1) the systematic sampling strategy, where the samples are obtained by selecting an element of the production line and skipping s consecutive elements before selecting the next one; (2) the mixed sampling strategy where the samples elements are selected from the two consecutive rational subgroups. The sampling strategies always improves the chart's performance, except when only one variable is affected by the assignable cause and the observations of this variable are not autocorrelated. If only one element is skipped, the average run length (ARL) reduces in more than 30%, on average. If two elements are skipped, this number increases to 40%. With the mixed sample, the average reduction is 25% in the ARL / Doutor

A dieta é considerada um dos fatores que mais influencia o comportamento espacial dos primatas. Muitas pesquisas que abordam essa relação apresentam similaridades nos seus delineamentos, mas não existe uma metodologia padrão comum. Para compreender melhor a relação entre dieta e padrões espaciais dos primatas, é preciso investigar o efeito de alguns problemas metodológicos. No presente estudo, descrevemos quatro:o problema da descontinuidade do registro, que é o efeito da dependência temporal sobre registros distribuídos desigualmente ao longo do tempo; o problema de filtragem, que descreve a dificuldade para isolar o efeito da variável independente, dieta; o problema do fracionamento, que alerta sobre os perigos de transportar conclusões a grande escala com dados de pequena escala; e o problema da linearidade fechada, que discute a validade das medidas de superfície quando o tempo registrado é muito curto. Desenvolvemos uma metodologia para controlar esses problemas. A metodologia foi aplicada com registros da dieta e localizações de um grupo de Sapajus nigritus do Parque Estadual Carlos Botelho, São Paulo, coletados em dois períodos, 2007-2008 e 2009-2010. Também utilizamos um delineamento mais convencional e comparamos os resultados obtidos com ambas asmetodologias. Os resultados foram similares com ambos os delineamentos, mas em alguns aspectosa metodologia nova teve melhor desempenho. A dieta foi analisada utilizando as categorias alimentos agregados e dispersos. Essa classificação tem sido criticada pela amplitude das suas categorias, mas no presente estudo foi sensível a mudanças nos padrões espaciais de Sapajus. Os resultados não foram conclusivos com períodos grandes descontínuos, mas foram visíveis com períodos curtos e contínuos. Com o aumento de consumo de itens dispersos diminuiu a distância diária percorrida e o espaço foi utilizado de forma mais uniforme. As maiores áreas foram observadas com períodos de consumo misto. Os padrões espaciais desses primatas foram bem descritos com base na energia obtida e os custos do deslocamento / Diet is considered one of the most influential factors on primates spatial patterns. Many studies that have addressed this relationship present methodological similarities, but there is no common standard methodology. In order to better understand the relationship between diet and spatial patterns of primates we need to investigate the effect of some methodological problems. In thisstudy we describe four of these problems: the problem of the discontinuous data, that is, the effect of autocorrelation when observations are distributed unevenly over time; the filtering problem, that describes the difficulties to isolate the effect of the independent variable, in this case, the diet; the partialness problem, that calls our attention to the risk of making large scale conclusions based on small scale data; and the problem of fenced linearity, that discusses the validity of area estimations, when time sampling is too small. We developed a methodology to control these problems and tested it on the data collected for one group of Sapajus nigritus in Carlos Botelhos State Park, São Paulo (Brazil), during two periods, 2007-2008 and 2009-2010. We also used a more conventional methodology to compare results. Although the results obtained using both methodologies were similar, in some cases, the new one performed better. Diet was analyzed byusing the categories patchy and dispersed food items. This dichotomous classification has been criticized because of the broadness of its categories, but in the present study it was sensitive to changes in Sapajus spatial patterns. Results were inconclusive when analyzing data from large discontinuous periods, but some conclusions were obtained when considering data from short continuous periods: daily path length decreased and the use of space was more uniform with the increase of dispersed items on the diet. The largest ranging areas were observed when the diet was mixed. Spatial patterns of these primates can be explained in terms of energy obtained and travel costs

by Wai Ho Mow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 116-124). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Spread Spectrum Technique --- p.2 / Chapter 1.1.1 --- Pulse Compression Radars --- p.3 / Chapter 1.1.2 --- Spread Spectrum Multiple Access Systems --- p.6 / Chapter 1.2 --- Definitions and Notations --- p.8 / Chapter 1.3 --- Organization of this Thesis --- p.12 / Chapter 2 --- Lower Bounds on Correlation of Sequences --- p.15 / Chapter 2.1 --- Welch's Lower Bounds and Sarwate's Generalization --- p.16 / Chapter 2.2 --- A New Construction and Bounds on Odd Correlation --- p.23 / Chapter 2.3 --- Known Sequence Sets Touching the Correlation Bounds --- p.26 / Chapter 2.4 --- Remarks on Other Bounds --- p.27 / Chapter 3 --- Perfect Polyphase Sequences: A Unified Approach --- p.29 / Chapter 3.1 --- Generalized Bent Functions and Perfect Polyphase Sequences --- p.30 / Chapter 3.2 --- The General Construction of Chung and Kumar --- p.32 / Chapter 3.3 --- Classification of Known Constructions ...........； --- p.34 / Chapter 3.4 --- A Unified Construction --- p.39 / Chapter 3.5 --- Desired Properties of Sequences --- p.41 / Chapter 3.6 --- Proof of the Main Theorem --- p.45 / Chapter 3.7 --- Counting the Number of Perfect Polyphase Sequences --- p.49 / Chapter 3.8 --- Results of Exhaustive Searches --- p.53 / Chapter 3.9 --- A New Conjecture and Its Implications --- p.55 / Chapter 3.10 --- Sets of Perfect Polyphase Sequences --- p.58 / Chapter 4 --- Aperiodic Autocorrelation of Generalized P3/P4 Codes --- p.61 / Chapter 4.1 --- Some Famous Polyphase Pulse Compression Codes --- p.62 / Chapter 4.2 --- Generalized P3/P4 Codes --- p.65 / Chapter 4.3 --- Asymptotic Peak-to-Side-Peak Ratio --- p.66 / Chapter 4.4 --- Lower Bounds on Peak-to-Side-Peak Ratio --- p.67 / Chapter 4.5 --- Even-Odd Transformation and Phase Alphabet --- p.70 / Chapter 5 --- Upper Bounds on Partial Exponential Sums --- p.77 / Chapter 5.1 --- Gauss-like Exponential Sums --- p.77 / Chapter 5.1.1 --- Background --- p.79 / Chapter 5.1.2 --- Symmetry of gL(m) and hL(m) --- p.80 / Chapter 5.1.3 --- Characterization on the First Quarter of gL(m) --- p.83 / Chapter 5.1.4 --- Characterization on the First Quarter of hL(m) --- p.90 / Chapter 5.1.5 --- Bounds on the Diameters of GL(m) and HL(m) --- p.94 / Chapter 5.2 --- More General Exponential Sums --- p.98 / Chapter 5.2.1 --- A Result of van der Corput --- p.99 / Chapter 6 --- McEliece's Open Problem on Minimax Aperiodic Correlation --- p.102 / Chapter 6.1 --- Statement of the Problem --- p.102 / Chapter 6.2 --- A Set of Two Sequences --- p.105 / Chapter 6.3 --- A Set of K Sequences --- p.110 / Chapter 7 --- Conclusion --- p.113 / Bibliography --- p.124