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Abstract: In this paper we describe how to conduct a change-point analysis when dealing with time series imprecisely or vaguely observed, i.e. time ordered observations whose values are not known exactly, such as interval or ordinal time series (imprecise time series). In order to treat such time series, we propose to employ a fuzzy approach i.e. data are parameterized in the form of fuzzy variables. Then, to detect the number and location of change points we employ a deviation measure for fuzzy variables in the framework of Atheoretical Regression Trees (ART). We present simulation results pertaining to the behavior of the proposed approach as well as two empirical applications to real imprecise time series. [Copyright &y& Elsevier]

Abstract: This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version. [Copyright &y& Elsevier]

• We present financial time series as Interval-Valued Time Series. • We deal with a multiple structural breaks detection problem. • We employ a Atheoretical Regression Trees method. • We empirically validate the proposal by detecting the breaks of a stock prices series. Multiple structural breaks detection for Interval-Valued Time Series (IVTS) is undoubtedly relevant under practical perspectives and challenging under the point of view of the analysis of expert systems. In this respect, financial time series usually show high variability and outliers; moreover, they often exhibit the property of being of high frequency nature; thus, it is naturally advisable to consider them as IVTS type for a given time unit. Despite this relevance, scarce effort has been spent by scholars to apply the methodological advancements in breaks detection for IVTS to the crucial environment of financial time series. This paper contributes to fill this gap. It employs the Atheoretical Regression Trees framework – a very recent tool that is able to automatically locale multiple breaks occurring to unknown dates – to stock prices. Such a procedure is able to estimate in an efficient way the structural breaks of the considered series; at the same time, it keeps into account the main characteristics of the intervals describing the IVTS. For our purposes, we adopt a theoretical proposal of reading daily stock prices as intervals whose bounds are defined through the closing prices. Empirical experiments on the American International Group – whose daily prices have experienced structural breaks in the past – validate the theoretical model and show the usefulness of the proposed procedure. [ABSTRACT FROM AUTHOR]