Detecting long-range dependence in non-stationary time series
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Date
2013-12-18
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Abstract
An important problem in time series analysis is the discrimination between non-stationarity and longrange
dependence. Most of the literature considers the problem of testing specificc parametric hypotheses of
non-stationarity (such as a change in the mean) against long-range dependent stationary alternatives. In
this paper we suggest a simple nonparametric approach, which can be used to test the null-hypothesis of a
general non-stationary short-memory against the alternative of a non-stationary long-memory process. This
test is working in the spectral domain and uses a sieve of approximating tvFARIMA models to estimate
the time varying long-range dependence parameter nonparametrically. We prove uniform consistency of this
estimate and asymptotic normality of an averaged version. These results yield a simple test (based on the
quantiles of the standard normal distribution), and it is demonstrated in a simulation study that - despite of
its nonparametric nature - the new test outperforms the currently available methods, which are constructed
to discriminate between speci fic parametric hypotheses of non-stationarity short- and stationarity long-range
dependence.
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Keywords
spectral density, sieve method, locally stationary process, integrated periodogram, empirical spectral measure, goodness-of- fit tests, non-stationary processes, long-memory