8,723 research outputs found
Long Range Dependence for Stable Random Processes
We investigate long and short memory in -stable moving averages and
max-stable processes with -Fr\'echet marginal distributions. As these
processes are heavy-tailed, we rely on the notion of long range dependence
suggested by Kulik and Spodarev (2019) based on the covariance of excursions.
Sufficient conditions for the long and short range dependence of
-stable moving averages are proven in terms of integrability of the
corresponding kernel functions. For max-stable processes, the extremal
coefficient function is used to state a necessary and sufficient condition for
long range dependence
Long-Range Dependence in Daily Interest Rate
We employ a number of parametric and non-parametric techniques to
establish the existence of long-range dependence in daily interbank o er
rates for four countries. We test for long memory using classical R=S
analysis, variance-time plots and Lo's (1991) modi ed R=S statistic. In
addition we estimate the fractional di erencing parameter using Whittle's
(1951) maximum likelihood estimator and we shu e the data to destroy
long and short memory in turn, and we repeat our non-parametric tests.
From our non-parametric tests we And strong evidence of the presence of
long memory in all four series independently of the chosen statistic. We
nd evidence that supports the assertion of Willinger et al (1999) that
Lo's statistic is biased towards non-rejection of the null hypothesis of no
long-range dependence. The parametric estimation concurs with these
results. Our results suggest that conventional tests for capital market
integration and other similar hypotheses involving nominal interest rates
should be treated with cautio
Detecting long-range dependence in non-stationary time series
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 specific 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 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. The test procedure works
in the spectral domain and uses a sequence of approximating tvFARIMA models to
estimate the time varying long-range dependence parameter. 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 semi-parametric nature - the new test outperforms the currently
available methods, which are constructed to discriminate between specific
parametric hypotheses of non-stationarity short- and stationarity long-range
dependence.Comment: Keywords and phrases: spectral density, long-memory, non-stationary
processes, goodness-of-fit tests, empirical spectral measure, integrated
periodogram, locally stationary process, approximating model
Asymptotic optimal designs under long-range dependence error structure
We discuss the optimal design problem in regression models with long-range
dependence error structure. Asymptotic optimal designs are derived and it is
demonstrated that these designs depend only indirectly on the correlation
function. Several examples are investigated to illustrate the theory. Finally,
the optimal designs are compared with asymptotic optimal designs which were
derived by Bickel and Herzberg [Ann. Statist. 7 (1979) 77--95] for regression
models with short-range dependent error.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ185 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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