281 research outputs found
Projective stochastic equations and nonlinear long memory
A projective moving average is a Bernoulli shift
written as a backward martingale transform of the innovation sequence. We
introduce a new class of nonlinear stochastic equations for projective moving
averages, termed projective equations, involving a (nonlinear) kernel and a
linear combination of projections of on "intermediate" lagged innovation
subspaces with given coefficients . The class of such
equations include usual moving-average processes and the Volterra series of the
LARCH model. Solvability of projective equations is studied, including a nested
Volterra series representation of the solution . We show that under
natural conditions on , this solution exhibits
covariance and distributional long memory, with fractional Brownian motion as
the limit of the corresponding partial sums process
Anisotropic scaling of random grain model with application to network traffic
We obtain a complete description of anisotropic scaling limits of random
grain model on the plane with heavy tailed grain area distribution. The scaling
limits have either independent or completely dependent increments along one or
both coordinate axes and include stable, Gaussian and some `intermediate'
infinitely divisible random fields. Asymptotic form of the covariance function
of the random grain model is obtained. Application to superposed network
traffic is included
Scaling transition for nonlinear random fields with long-range dependence
We obtain a complete description of anisotropic scaling limits and the
existence of scaling transition for nonlinear functions (Appell polynomials) of
stationary linear random fields on with moving average
coefficients decaying at possibly different rate in the horizontal and vertical
direction. The paper extends recent results on scaling transition for linear
random fields in Puplinskait\.e and Surgailis (2016), Puplinskait\.e and
Surgailis (2015)
Nonparametric estimation of the local Hurst function of multifractional Gaussian processes
A new nonparametric estimator of the local Hurst function of a
multifractional Gaussian process based on the increment ratio (IR) statistic is
defined. In a general frame, the point-wise and uniform weak and strong
consistency and a multidimensional central limit theorem for this estimator are
established. Similar results are obtained for a refinement of the generalized
quadratic variations (QV) estimator. The example of the multifractional
Brownian motion is studied in detail. A simulation study is included showing
that the IR-estimator is more accurate than the QV-estimator
A two-sample test for comparison of long memory parameters
We construct a two-sample test for comparison of long memory parameters based
on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L.,
Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit
roots for a wide class of dependent errors. Econometric Theory 21, 989--1029].
The two samples have the same length and can be mutually independent or
dependent. In the latter case, the test statistic is modified to make it
asymptotically free of the long-run correlation coefficient between the
samples. To diminish the sensitivity of the test on the choice of the bandwidth
parameter, an adaptive formula for the bandwidth parameter is derived using the
asymptotic expansion in [Abadir, K., Distaso, W., Giraitis, L., 2009. Two
estimators of the long-run variance: Beyond short memory. Journal of
Econometrics 150, 56--70]. A simulation study shows that the above choice of
bandwidth leads to a good size of our comparison test for most values of
fractional and ARMA parameters of the simulated series
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