Statistical inference in time series analysis has been an important subject in various fields including climate science, economics, finance and industrial engineering among others. Numerous problems of research interest include statistical inference about unknown quantities, assessing structural stability and forecasting. These problems have been widely studied in the literature, but mainly for independent data, while in many applications involving time series data dependence is not unusual and in fact quite common. In this thesis, we incorporate serial dependence into the analysis by involving self-normalization in time series analysis. We start with the problem of testing whether there are change-points in a given time series. The method we propose does not require the number of change-points to be predefined, and thus is unsupervised. It does not require any tuning parameters and can be applied to a wide class to quantities of interest. The asymptotic distribution of the test statistic is studied and an approximation scheme is proposed to reduce testing procedure complexity. We then consider the problem of construction of confidence intervals, for which the conventional self-normalizer exhibits certain degrees of asymmetry when applied to quantities other than the mean. The method we propose provides a time-symmetric generalization to the conventional self-normalizer and leads to improved finite sample performance for quantities other than the mean.

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

Master of Science / Department of Chemistry / Christopher T. Culbertson / Circulating tumor cells (CTCs) have become a key component in the identification and treatment of cancer. Once dislodged from the main tumor, CTCs travel through the bloodstream and cause metastasis. Early detection and identification of these cells can help in the evaluation and prognosis of various types of cancer, as well as assisting in patient treatments by determining the spread of the disease. Here, a high-throughput microfluidic analysis technique is described that can efficiently detect and identify cells, with the specific identification of CTCs as a future application through fluorescent labeling in mind. As proof of principle, the device has been shown to detect and characterize individual human Jurkat (T-lymphocyte) cells at a rate of 100 cells/minute. The device employs micro-scale flow focusing to isolate individual cells. The cells are detected using both light scattering and laser-induced fluorescence to evaluate cell size and surface functionality.

Evidence of networks in the resting-brain reflecting the spontaneous brain activity is perhaps the most significant discovery to understand intrinsic brain functionality. Moreover, subsequent detection of dynamics in these networks can be milestone in differentiating the normal and disordered brain functions. However, capturing the correct dynamics is a challenging task since no ground truths' are present for comparison of the results. The change points of these networks can be different for different subjects even during normal brain functions. Even for the same subject and session, dynamics can be different at the start and end of the session based on the fatigue level of the subject scanned. Despite the absence of ground truths, studies have analyzed these dynamics using the existing methods and some of them have developed new algorithms too. One of the most commonly used method for this purpose is sliding window correlation. However, the result of the sliding window correlation is dependent on many parameters and without the ground truth there is no way of validating the results. In addition, most of the new algorithms are complicated, computationally expensive, and/or focus on just one aspect on these dynamics. This study applies the algorithms and concepts from signal processing, image processing, video processing, information theory, and machine learning to analyze the results of the sliding window correlation and develops a novel algorithm to detect change points of these networks adaptively. The findings in this study are divided into three parts: 1) Analyzing the extent of variability in well-defined networks of rodents and humans with sliding window correlation applying concepts from information theory and machine learning domains. 2) Analyzing the performance of sliding window correlation using simulated networks as ground truths for best parameters’ selection, and exploring its dependence on multiple frequency components of the correlating signals by processing the signals in time and Fourier domains. 3) Development of a novel algorithm based on image similarity measures from image and video processing that maybe employed to identify change points of these networks adaptively.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In this research work, auto-associative neural networks have been used for changepoint detection. This is a nonlinear technique that employs the use of artificial neural networks as inspired among other by Frank Rosenblatt’s linear perceptron algorithm for classification. An auto-associative neural network was used successfully to detect change-points for various types of time series data. Its performance was compared to that of singular spectrum analysis developed by Moskvina and Zhigljavsky. Fraction of Explained Variance (FEV) was also used to compare the performance of the two methods. FEV indicators are similar to the eigenvalues of the covariance matrix in principal component analysis. Two types of time series data were used for change-point detection: Gaussian data series and nonlinear reaction data series. The Gaussian data had four series with different types of change-points, namely a change in the mean value of the time series (T1), a change in the variance of the time series (T2), a change in the autocorrelation of the time series (T3), and a change in the crosscorrelation of two time series (T4). Both linear and nonlinear methods were able to detect the changes for T1, T2 and T4. None of them could detect the changes in T3. With the Gaussian data series, linear singular spectrum analysis (LSSA) performed as well as the NLSSA for the change point detection. This is because the time series was linear and the nonlinearity of the NLSSA was therefore not important. LSSA did even better than NLSSA when comparing FEV values, since it is not subject to suboptimal solutions as could sometimes be the case with autoassociative neural networks. The nonlinear data consisted of the Belousov-Zhabotinsky (BZ) reactions, autocatalytic reaction time series data and data representing a predator-prey system. With the NLSSA methods, change points could be detected accurately in all three systems, while LSSA only managed to detect the change-point on the BZ reactions and the predator-prey system. The NLSSA method also fared better than the LSSA method when comparing FEV values for the BZ reactions. The LSSA method was able to model the autocatalytic reactions fairly accurately, being able to explain 99% of the variance in the data with one component only. NLSSA with two nodes on the bottleneck attained an FEV of 87%. The performance of both NLSSA and LSSA were comparable for the predator-prey system, both systems, where both could attain FEV values of 92% with a single component. An auto-associative neural network is a good technique for change point detection in nonlinear time series data. However, it offers no advantage over linear techniques when the time series data are linear. / AFRIKAANSE OPSOMMING: In hierdie navorsing is outoassosiatiewe neurale netwerk gebruik vir veranderingspuntwaarneming. Dis is ‘n nielineêre tegniek wat neurale netwerke gebruik soos onder andere geïnspireer deur Frank Rosnblatt se lineêre perseptronalgoritme vir klassifikasie. ‘n Outoassosiatiewe neurale netwerk is suksesvol gebruik om veranderingspunte op te spoor in verskeie tipes tydreeksdata. Die prestasie van die outoassosiatiewe neurale netwerk is vergelyk met singuliere spektrale oontleding soos ontwikkel deur Moskvina en Zhigljavsky. Die fraksie van die verklaarde variansie (FEV) is ook gebruik om die prestasie van die twee metodes te vergelyk. FEV indikatore is soortgelyk aan die eiewaardes van die kovariansiematriks in hoofkomponentontleding. Twee tipes tydreeksdata is gebruik vir veranderingspuntopsporing: Gaussiaanse tydreekse en nielineêre reaksiedatareekse. Die Gaussiaanse data het vier reekse gehad met verskillende veranderingspunte, naamlik ‘n verandering in die gemiddelde van die tydreeksdata (T1), ‘n verandering in die variansie van die tydreeksdata (T2), ‘n verandering in die outokorrelasie van die tydreeksdata (T3), en ‘n verandering in die kruiskorrelasie van twee tydreekse (T4). Beide lineêre en nielineêre metodes kon die veranderinge in T1, T2 en T4 opspoor. Nie een het egter daarin geslaag om die verandering in T3 op te spoor nie. Met die Gaussiaanse tydreeks het lineêre singuliere spektrumanalise (LSSA) net so goed gevaar soos die outoassosiatiewe neurale netwerk of nielineêre singuliere spektrumanalise (NLSSA), aangesien die tydreekse lineêr was en die vermoë van die NLSSA metode om nielineêre gedrag te identifiseer dus nie belangrik was nie. Inteendeel, die LSSA metode het ‘n groter FEV waarde getoon as die NLSSA metode, omdat LSSA ook nie blootgestel is aan suboptimale oplossings, soos wat soms die geval kan wees met die afrigting van die outoassosiatiewe neural netwerk nie. Die nielineêre data het bestaan uit die Belousov-Zhabotinsky (BZ) reaksiedata, ‘n outokatalitiese reaksietydreeksdata en data wat ‘n roofdier-prooistelsel verteenwoordig het. Met die NLSSA metode kon veranderingspunte betroubaar opgespoor word in al drie tydreekse, terwyl die LSSA metode net die veranderingspuntin die BZ reaksie en die roofdier-prooistelsel kon opspoor. Die NLSSA metode het ook beter gevaaar as die LSSA metode wanneer die FEV waardes vir die BZ reaksies vergelyk word. Die LSSA metode kon die outokatalitiese reaksies redelik akkuraat modelleer, en kon met slegs een komponent 99% van die variansie in die data verklaar. Die NLSSA metode, met twee nodes in sy bottelneklaag, kon ‘n FEV waarde van slegs 87% behaal. Die prestasie van beide metodes was vergelykbaar vir die roofdier-prooidata, met beide wat FEV waardes van 92% kon behaal met hulle een komponent. ‘n Outoassosiatiewe neural netwerk is ‘n goeie metode vir die opspoor van veranderingspunte in nielineêre tydreeksdata. Dit hou egter geen voordeel in wanneer die data lineêr is nie.

Title: Statistical analysis of historical temperature series Author: Václav Gergelits Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jaromír Antoch CSc. Supervisor's e-mail address: antoch@karlin.mff.cuni.cz Abstract: In the present work we deal with the statistical analysis of time-series of a mean-temperature obtained from seven European cities from the Europe Union project "IMPROVE". Properties of the time series are analyzed by means of descriptive statistics, being assessing their homoscedasticity, autocorrelation and normality. We report the ways in which the data has been adjusted, including consideration of the impact of the urban heat island and we discuss the availability of additional data. The theoretical part presents a theory of change point detection for a one change model as well as more than one change model taking an autocorrelation into account. In the practical part we analyze the data using change point detection method. The significant increase was not detected for time series of Cadiz and Uppsala. The significant increase was rather detected for the rest of the time series. The increase of temperature could be in a relation to the adjustment for the urban heat island. Keywords: change point detection, temperature time series 1

<p>The distribution of asset returns may lead to structural breaks. Thesebreaks may result in changes of the optimal portfolio weights. For a port-folio investor, the ability of timely detection of any systematic changesin the optimal portfolio weights is of a great interest.In this master thesis work, the use of the Shewhart method, as amethod for detecting a sudden parameter change, the implied changein the multivariate portfolio weights and its performance is reviewed.</p><p> </p>

The use of solar cells for energy production has indeed a bright future. Reduction of cost for fabrication along with increased efficiency are key features for a market boom, both achieved as a result of increased knowledge of the technology. Especially the thin film solar cell technology with absorbers made of Cu(In,Ga)Se2 (CIGS) is promising since it has proven high power conversion efficiency in combination with a true potential for low cost fabrication. In this thesis different recipes for fabrication of the Cu(In,Ga)Se2 absorber layer have been studied. The deposition technique used has been co-evaporation from elemental sources. For all depositions the substrate has been heated to a constant temperature of 500 ºC in order for the growing absorber to form a chalcopyrite phase, necessary for the photovoltaic functionality. The selenium has been evaporated such to always be in excess during depositions whereas the metal ratio Cu/(In+Ga) has been varied according to different recipes but always to be less than one at the end of the process. In the work emphasis has been on the radiative properties of the CIGS film during growth. The substrate heater has been temperature controlled to maintain the constant set temperature of the substrate, regardless of varying emitted power caused by changing surface emissivity. Depending on the growth conditions the emissivity of the growing film is changing, leading to a readable variation in the electrical power to the substrate heater. Since the thermal radiation from the substrate during growth has been of central focus, this has been studied in detail. For this reason the substrate has been treated as an optical stack composed of glass/Mo/Cu(In,Ga)Se2/CuxSe which determine the thermally radiated power by its emissivity. An optical model has been adopted to simulate the emissivity of the stack. In order to use the model, the optical constants for Cu(In,Ga)Se2 and CuxSe have been derived for the wavelength interval 2 μm to 20 μm. The simulation of the emissivity of the stack during CIGS growth agreed well with what has been seen for actual growth. Features of the OP-signal could hereby be explained as a result of film thickness of Cu(In,Ga)Se2 and CuxSe respectively. This is an important knowledge for an efficient fabrication in large scale.

In this thesis we investigate the case of monitoring of stocks havingjust been introduced for public trading on the nancial market. Theempirical distribution of the change-point for 20 assets for 60 days was calculated to check the support for the assumption that the priceinitially drop or rise to some steady level.The price process X = {Xt : t in Z} is assumed to be an AR(1) process with a shift in the mean value from a slope to a constant. The Shiryaev-Roberts, Shewhart, EWMA, Likelihood ratio and CUSUM proceduresfor detecting a change-point in such a process are derived. The expecteddelay of the motivated alarm according to these methods is achievedunder the assumptions of a Poisson, uniform, binomial and geometric distributed by means of simulations.

Consider a time series model which is stationary apart from a single shift in mean. If the time of a level shift is known, the least squares estimator of the magnitude of this level shift is a minimum variance unbiased estimator. If the time is unknown, however, this estimator is biased. Here, we first carry out extensive simulation studies to determine the relationship between the bias and three parameters of our time series model: the true magnitude of the level shift, the true time point and the autocorrelation of adjacent observations. Thereafter, we use two generalized additive models to generalize the simulation results. Finally, we examine to what extent the bias can be reduced by multiplying the least squares estimator with a shrinkage factor. Our results showed that the bias of the estimated magnitude of the level shift can be reduced when the level shift does not occur close to the beginning or end of the time series. However, it was not possible to simultaneously reduce the bias for all possible time points and magnitudes of the level shift.