141 research outputs found
Ratio tests for change point detection
We propose new tests to detect a change in the mean of a time series. Like
many existing tests, the new ones are based on the CUSUM process. Existing
CUSUM tests require an estimator of a scale parameter to make them
asymptotically distribution free under the no change null hypothesis. Even if
the observations are independent, the estimation of the scale parameter is not
simple since the estimator for the scale parameter should be at least
consistent under the null as well as under the alternative. The situation is
much more complicated in case of dependent data, where the empirical spectral
density at 0 is used to scale the CUSUM process. To circumvent these
difficulties, new tests are proposed which are ratios of CUSUM functionals. We
demonstrate the applicability of our method to detect a change in the mean when
the errors are AR(1) and GARCH(1,1) sequences.Comment: Published in at http://dx.doi.org/10.1214/193940307000000220 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
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
Structural Change in (Economic) Time Series
Methods for detecting structural changes, or change points, in time series
data are widely used in many fields of science and engineering. This chapter
sketches some basic methods for the analysis of structural changes in time
series data. The exposition is confined to retrospective methods for univariate
time series. Several recent methods for dating structural changes are compared
using a time series of oil prices spanning more than 60 years. The methods
broadly agree for the first part of the series up to the mid-1980s, for which
changes are associated with major historical events, but provide somewhat
different solutions thereafter, reflecting a gradual increase in oil prices
that is not well described by a step function. As a further illustration, 1990s
data on the volatility of the Hang Seng stock market index are reanalyzed.Comment: 12 pages, 6 figure
Asymptotics of trimmed CUSUM statistics
There is a wide literature on change point tests, but the case of variables
with infinite variances is essentially unexplored. In this paper we address
this problem by studying the asymptotic behavior of trimmed CUSUM statistics.
We show that in a location model with i.i.d. errors in the domain of attraction
of a stable law of parameter , the appropriately trimmed CUSUM
process converges weakly to a Brownian bridge. Thus, after moderate trimming,
the classical method for detecting change points remains valid also for
populations with infinite variance. We note that according to the classical
theory, the partial sums of trimmed variables are generally not asymptotically
normal and using random centering in the test statistics is crucial in the
infinite variance case. We also show that the partial sums of truncated and
trimmed random variables have different asymptotic behavior. Finally, we
discuss resampling procedures which enable one to determine critical values in
the case of small and moderate sample sizes.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ318 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Quickest detection in coupled systems
This work considers the problem of quickest detection of signals in a coupled
system of N sensors, which receive continuous sequential observations from the
environment. It is assumed that the signals, which are modeled a general Ito
processes, are coupled across sensors, but that their onset times may differ
from sensor to sensor. The objective is the optimal detection of the first time
at which any sensor in the system receives a signal. The problem is formulated
as a stochastic optimization problem in which an extended average Kullback-
Leibler divergence criterion is used as a measure of detection delay, with a
constraint on the mean time between false alarms. The case in which the sensors
employ cumulative sum (CUSUM) strategies is considered, and it is proved that
the minimum of N CUSUMs is asymptotically optimal as the mean time between
false alarms increases without bound.Comment: 6 pages, 48th IEEE Conference on Decision and Control, Shanghai 2009
December 16 - 1
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