Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

The aim of this study was to evaluate the performance of a classical method of fractal analysis, Detrended Fluctuation Analysis (DFA), in the analysis of the dynamics of animal behavior time series. In order to correctly use DFA to assess the presence of long-range correlation, previous authors using statistical model systems have stated that different aspects should be taken into account such as: 1) the establishment by hypothesis testing of the absence of short term correlation, 2) an accurate estimation of a straight line in the log-log plot of the fluctuation function, 3) the elimination of artificial crossovers in the fluctuation function, and 4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail ({\sl Coturnix coturnix}) and mosquito larva ({\sl Culex quinquefasciatus}). In our study, modeling the data with the general ARFIMA model, we rejected the hypothesis of short range correlations (d=0) in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail, and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations

Ultra high frequency volatility estimation with dependent microstructure noise

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility. --Market microstructure,Serial dependence,High frequency data,Realized volatility,Subsampling,Two Scales Realized Volatility

Towards Handling Uncertainty in Prognostic Scenarios: Advanced Learning from the Past

Das Forschungsprogramm „Earth System Sciences (ESS)“, ein Programm des Bundesministeriums für Wissenschaft, Forschung und Wirtschaft (BMWFW), durchgeführt von der ÖAW, hat die Erforschung des Systems Erde zum Ziel. Im Rahmen von Ausschreibungen werden wissenschaftliche Forschungsprojekte gefördert, die dem neusten Stand der Wissenschaft entsprechen. Das Programm ESS sieht es als seine Aufgabe, Lücken in der österreichischen Förderungslandschaft zu schließen. Dies bezieht sich etwa auf interdisziplinäre Projekte, Projekte zur Langzeitforschung sowie auf Projekte, die auf derzeit noch gering beforschte Bereiche fokussiert sind und denen wissenschaftlich

Lorenz-based quantitative risk management

In this thesis, we address problems of quantitative risk management using a specific set of tools that go under the name of Lorenz curve and inequality indices, developed to describe the socio-economic variability of a random variable.Quantitative risk management deals with the estimation of the uncertainty that isembedded in the activities of banks and other financial players due, for example, tomarket fluctuations. Since the well-being of such financial players is fundamental for the correct functioning of the economic system, an accurate description and estimation of such uncertainty is crucial.Applied ProbabilityNumerical Analysi

Quantum Tomography

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"Comment: To appear in "Advances in Imaging and Electron Physics". Some figs with low resolutio