55 research outputs found
Estimators for epidemic alternatives
summary:We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation
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
Simultaneous rank test procedures
summary:Simultaneous rank test procedures are proposed for testing of randomness concerning some marginals. The considered test procedures are analogous to those introduced by Krishnaiah for classical normal theory (see Krishnaiah (1965) Ann. Inst. Statist. Math. 17, 35-53)
Testing for changes in polynomial regression
We consider a nonlinear polynomial regression model in which we wish to test
the null hypothesis of structural stability in the regression parameters
against the alternative of a break at an unknown time. We derive the extreme
value distribution of a maximum-type test statistic which is asymptotically
equivalent to the maximally selected likelihood ratio. The resulting test is
easy to apply and has good size and power, even in small samples.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ122 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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Structural breaks in panel data: large number of panels and short length time series
The detection of (structural) breaks or the so called change point problem has drawn increasing attention from the theoretical, applied economic and financial fields. Much of the existing research concentrates on the detection of change points and asymptotic properties of their estimators in panels when N, the number of panels, as well as T, the number of observations in each panel are large. In this paper we pursue a different approach, i.e., we consider the asymptotic properties when N→∞ while keeping T fixed. This situation is typically related to large (firm-level) data containing financial information about an immense number of firms/stocks across a limited number of years/quarters/months. We propose a general approach for testing for break(s) in this setup. In particular, we obtain the asymptotic behavior of test statistics. We also propose a wild bootstrap procedure that could be used to generate the critical values of the test statistics. The theoretical approach is supplemented by numerous simulations and by an empirical illustration. We demonstrate that the testing procedure works well in the framework of the four factors CAPM model. In particular, we estimate the breaks in the monthly returns of US mutual funds during the period January 2006 to February 2010 which covers the subprime crises
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