116 research outputs found
Change-Point Testing and Estimation for Risk Measures in Time Series
We investigate methods of change-point testing and confidence interval
construction for nonparametric estimators of expected shortfall and related
risk measures in weakly dependent time series. A key aspect of our work is the
ability to detect general multiple structural changes in the tails of time
series marginal distributions. Unlike extant approaches for detecting tail
structural changes using quantities such as tail index, our approach does not
require parametric modeling of the tail and detects more general changes in the
tail. Additionally, our methods are based on the recently introduced
self-normalization technique for time series, allowing for statistical analysis
without the issues of consistent standard error estimation. The theoretical
foundation for our methods are functional central limit theorems, which we
develop under weak assumptions. An empirical study of S&P 500 returns and US
30-Year Treasury bonds illustrates the practical use of our methods in
detecting and quantifying market instability via the tails of financial time
series during times of financial crisis
Change Point Testing for the Drift Parameters of a Periodic Mean Reversion Process
In this paper we investigate the problem of detecting a change in the drift
parameters of a generalized Ornstein-Uhlenbeck process which is defined as the
solution of , and which is observed in
continuous time. We derive an explicit representation of the generalized
likelihood ratio test statistic assuming that the mean reversion function
is a finite linear combination of known basis functions. In the case of
a periodic mean reversion function, we determine the asymptotic distribution of
the test statistic under the null hypothesis
Deciphering hierarchical organization of topologically associated domains through change-point testing.
BACKGROUND: The nucleus of eukaryotic cells spatially packages chromosomes into a hierarchical and distinct segregation that plays critical roles in maintaining transcription regulation. High-throughput methods of chromosome conformation capture, such as Hi-C, have revealed topologically associating domains (TADs) that are defined by biased chromatin interactions within them.
RESULTS: We introduce a novel method, HiCKey, to decipher hierarchical TAD structures in Hi-C data and compare them across samples. We first derive a generalized likelihood-ratio (GLR) test for detecting change-points in an interaction matrix that follows a negative binomial distribution or general mixture distribution. We then employ several optimal search strategies to decipher hierarchical TADs with p values calculated by the GLR test. Large-scale validations of simulation data show that HiCKey has good precision in recalling known TADs and is robust against random collisions of chromatin interactions. By applying HiCKey to Hi-C data of seven human cell lines, we identified multiple layers of TAD organization among them, but the vast majority had no more than four layers. In particular, we found that TAD boundaries are significantly enriched in active chromosomal regions compared to repressed regions.
CONCLUSIONS: HiCKey is optimized for processing large matrices constructed from high-resolution Hi-C experiments. The method and theoretical result of the GLR test provide a general framework for significance testing of similar experimental chromatin interaction data that may not fully follow negative binomial distributions but rather more general mixture distributions
Robust mean change point testing in high-dimensional data with heavy tails
We study a mean change point testing problem for high-dimensional data, with
exponentially- or polynomially-decaying tails. In each case, depending on the
-norm of the mean change vector, we separately consider dense and
sparse regimes. We characterise the boundary between the dense and sparse
regimes under the above two tail conditions for the first time in the change
point literature and propose novel testing procedures that attain optimal rates
in each of the four regimes up to a poly-iterated logarithmic factor. Our
results quantify the costs of heavy-tailedness on the fundamental difficulty of
change point testing problems for high-dimensional data by comparing to the
previous results under Gaussian assumptions.
To be specific, when the error vectors follow sub-Weibull distributions, a
CUSUM-type statistic is shown to achieve a minimax testing rate up to
. When the error distributions have polynomially-decaying
tails, admitting bounded -th moments for some , we
introduce a median-of-means-type test statistic that achieves a near-optimal
testing rate in both dense and sparse regimes. In particular, in the sparse
regime, we further propose a computationally-efficient test to achieve the
exact optimality. Surprisingly, our investigation in the even more challenging
case of , unveils a new phenomenon that the minimax testing
rate has no sparse regime, i.e. testing sparse changes is
information-theoretically as hard as testing dense changes. This phenomenon
implies a phase transition of the minimax testing rates at .Comment: 50 pages, 1 figur
Change point testing for the drift parameters of a periodic mean reversion process
In this paper we investigate the problem of detecting a change in the drift
parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of
dX_t = (L(t) - alpha X_t)dt + delta dB_t
and which is observed in continuous time. We derive an explicit representation of the
generalized likelihood ratio test statistic assuming that the mean reversion function L(t)
is a finite linear combination of known basis functions. In the case of a periodic mean
reversion function, we determine the asymptotic distribution of the test statistic under the
null hypothesis
Change-Point Tests for Precipitation Data
A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test statistic, methods are devoloped for testing for fixed and unknown change-points. These methods are developed for various models, including the MC/gamma model and simplified versions. The distribution of the LRT is unknown, however its asymptotic distribution is known for both the fixed and unknown change-point tests. First, the asymptotic converegence rates are analyzed using simulation, and then the power of the test is also analyzed using simulation. Finally the test is applied to real data, and the results are analyzed
Robust discrimination between long-range dependence and a change in mean
In this paper we introduce a robust to outliers Wilcoxon change-point testing procedure,
for distinguishing between short-range dependent time series with a change in mean at unknown
time and stationary long-range dependent time series. We establish the asymptotic
distribution of the test statistic under the null hypothesis for L1 near epoch dependent
processes and show its consistency under the alternative. The Wilcoxon-type testing procedure
similarly as the CUSUM-type testing procedure of Berkes, Horvath, Kokoszka and
Shao (2006), requires estimation of the location of a possible change-point, and then using
pre- and post-break subsamples to discriminate between short and long-range dependence.
A simulation study examines the empirical size and power of the Wilcoxon-type testing
procedure in standard cases and with disturbances by outliers. It shows that in standard
cases the Wilcoxon-type testing procedure behaves equally well as the CUSUM-type testing
procedure but outperforms it in presence of outliers
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