18,488 research outputs found
Heterogeneous Change Point Inference
We propose HSMUCE (heterogeneous simultaneous multiscale change-point
estimator) for the detection of multiple change-points of the signal in a
heterogeneous gaussian regression model. A piecewise constant function is
estimated by minimizing the number of change-points over the acceptance region
of a multiscale test which locally adapts to changes in the variance. The
multiscale test is a combination of local likelihood ratio tests which are
properly calibrated by scale dependent critical values in order to keep a
global nominal level alpha, even for finite samples. We show that HSMUCE
controls the error of over- and underestimation of the number of change-points.
To this end, new deviation bounds for F-type statistics are derived. Moreover,
we obtain confidence sets for the whole signal. All results are non-asymptotic
and uniform over a large class of heterogeneous change-point models. HSMUCE is
fast to compute, achieves the optimal detection rate and estimates the number
of change-points at almost optimal accuracy for vanishing signals, while still
being robust. We compare HSMUCE with several state of the art methods in
simulations and analyse current recordings of a transmembrane protein in the
bacterial outer membrane with pronounced heterogeneity for its states. An
R-package is available online
Exploring the segmentation space for the assessment of multiple change-point models
This paper addresses the retrospective or off-line multiple change-point detection problem. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a forward dynamic programming algorithm for computing the top L most probable segmentations and a forward-backward algorithm for sampling segmentations are derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the space of possible segmentations for successive numbers of change points and provide a set of assessment tools for multiple change-point models. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the location of change points
Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations
This paper addresses the problem of detecting and characterizing local
variability in time series and other forms of sequential data. The goal is to
identify and characterize statistically significant variations, at the same
time suppressing the inevitable corrupting observational errors. We present a
simple nonparametric modeling technique and an algorithm implementing it - an
improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds
the optimal segmentation of the data in the observation interval. The structure
of the algorithm allows it to be used in either a real-time trigger mode, or a
retrospective mode. Maximum likelihood or marginal posterior functions to
measure model fitness are presented for events, binned counts, and measurements
at arbitrary times with known error distributions. Problems addressed include
those connected with data gaps, variable exposure, extension to piecewise
linear and piecewise exponential representations, multi-variate time series
data, analysis of variance, data on the circle, other data modes, and dispersed
data. Simulations provide evidence that the detection efficiency for weak
signals is close to a theoretical asymptotic limit derived by (Arias-Castro,
Donoho and Huo 2003). In the spirit of Reproducible Research (Donoho et al.
2008) all of the code and data necessary to reproduce all of the figures in
this paper are included as auxiliary material.Comment: Added some missing script files and updated other ancillary data
(code and data files). To be submitted to the Astophysical Journa
Filtered derivative with p-value method for multiple change-points detection
This paper deals with off-line detection of change points for time series of
independent observations, when the number of change points is unknown. We
propose a sequential analysis like method with linear time and memory
complexity. Our method is based at first step, on Filtered Derivative method
which detects the right change points but also false ones. We improve Filtered
Derivative method by adding a second step in which we compute the p-values
associated to each potential change points. Then we eliminate as false alarms
the points which have p-value smaller than a given critical level. Next, our
method is compared with the Penalized Least Square Criterion procedure on
simulated data sets. Eventually, we apply Filtered Derivative with p-Value
method to segmentation of heartbeat time series
Multiscale change-point segmentation: beyond step functions.
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning (minimax) estimation theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper, for a large collection of multiscale segmentation methods (including various existing procedures), such theory will be extended to certain function classes beyond step functions in a nonparametric regression setting. This extends the interpretation of such methods on the one hand and on the other hand reveals these methods as robust to deviation from piecewise constant functions. Our main finding is the adaptation over nonlinear approximation classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Holder functions of smoothness order 0 < alpha <= 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a log-factor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations
Off-line detection of multiple change points with the Filtered Derivative with p-Value method
This paper deals with off-line detection of change points for time series of
independent observations, when the number of change points is unknown. We
propose a sequential analysis like method with linear time and memory
complexity. Our method is based at first step, on Filtered Derivative method
which detects the right change points but also false ones. We improve Filtered
Derivative method by adding a second step in which we compute the p-values
associated to each potential change points. Then we eliminate as false alarms
the points which have p-value smaller than a given critical level. Next, our
method is compared with the Penalized Least Square Criterion procedure on
simulated data sets. Eventually, we apply Filtered Derivative with p-Value
method to segmentation of heartbeat time series, and detection of change points
in the average daily volume of financial time series
High-dimensional GARCH process segmentation with an application to Value-at-Risk
Models for financial risk often assume that underlying asset returns are
stationary. However, there is strong evidence that multivariate financial time
series entail changes not only in their within-series dependence structure, but
also in the cross-sectional dependence among them. In particular, the stressed
Value-at-Risk of a portfolio, a popularly adopted measure of market risk,
cannot be gauged adequately unless such structural breaks are taken into
account in its estimation. We propose a method for consistent detection of
multiple change points in high-dimensional GARCH panel data set where both
individual GARCH processes and their correlations are allowed to change over
time. We prove its consistency in multiple change point estimation, and
demonstrate its good performance through simulation studies and an application
to the Value-at-Risk problem on a real dataset. Our methodology is implemented
in the R package segMGarch, available from CRAN
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