Detecting smooth changes in locally stationary processes
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Date
2013-10-11
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Abstract
In a wide range of applications, the stochastic properties of the observed time
series change over time. It is often realistic to assume that the properties are
approximately the same over short time periods and then gradually start to vary.
This behaviour is well modelled by locally stationary processes. In this paper,
we investigate the question how to estimate time spans where the stochastic
features of a locally stationary time series are the same. We set up a general method which allows to deal with a wide variety of features including the
mean, covariances, higher moments and the distribution of the time series under
consideration. In the theoretical part of the paper, we derive the asymptotic
properties of our estimation method. In addition, we examine its finite sample
performance by means of a simulation study and illustrate the methodology by
an application to financial data.
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Keywords
empirical processes, local stationarity, measure of time-variation