351 research outputs found
On parameter estimation for locally stationary long-memory processes
We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth are obtained. In spite of long memory, the optimal bandwidth turns out to be of the order n^(-1/5) and inversely proportional to the square of the second derivative of d. In this sense, local estimation of d is comparable to regression smoothing with iid residuals.long memory, fractional ARIMA process, local stationarity, bandwidth selection
On estimating extremal dependence structures by parametric spectral measures
Estimation of extreme value copulas is often required in situations where
available data are sparse. Parametric methods may then be the preferred
approach. A possible way of defining parametric families that are simple and,
at the same time, cover a large variety of multivariate extremal dependence
structures is to build models based on spectral measures. This approach is
considered here. Parametric families of spectral measures are defined as convex
hulls of suitable basis elements, and parameters are estimated by projecting an
initial nonparametric estimator on these finite-dimensional spaces. Asymptotic
distributions are derived for the estimated parameters and the resulting
estimates of the spectral measure and the extreme value copula. Finite sample
properties are illustrated by a simulation study
On approximate pseudo-maximum likelihood estimation for LARCH-processes
Linear ARCH (LARCH) processes were introduced by Robinson [J. Econometrics 47
(1991) 67--84] to model long-range dependence in volatility and leverage. Basic
theoretical properties of LARCH processes have been investigated in the recent
literature. However, there is a lack of estimation methods and corresponding
asymptotic theory. In this paper, we consider estimation of the dependence
parameters for LARCH processes with non-summable hyperbolically decaying
coefficients. Asymptotic limit theorems are derived. A central limit theorem
with -rate of convergence holds for an approximate conditional
pseudo-maximum likelihood estimator. To obtain a computable version that
includes observed values only, a further approximation is required. The
computable estimator is again asymptotically normal, however with a rate of
convergence that is slower than Comment: Published in at http://dx.doi.org/10.3150/09-BEJ189 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
On asymptotically optimal wavelet estimation of trend functions under long-range dependence
We consider data-adaptive wavelet estimation of a trend function in a time
series model with strongly dependent Gaussian residuals. Asymptotic expressions
for the optimal mean integrated squared error and corresponding optimal
smoothing and resolution parameters are derived. Due to adaptation to the
properties of the underlying trend function, the approach shows very good
performance for smooth trend functions while remaining competitive with minimax
wavelet estimation for functions with discontinuities. Simulations illustrate
the asymptotic results and finite-sample behavior.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ332 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors
This paper summarizes recent developments in non- and semiparametric regres- sion with stationary fractional time series errors, where the error process may be short-range, long-range dependent or antipersistent. The trend function in this model is estimated nonparametrically, while the dependence structure of the error process is estimated by approximate maximum likelihood. Asymptotic properties of these estimators are described briefly. The focus is on describing the developments of bandwidth selection in this context based on the iterative plug-in idea (Gasser et al., 1991) and some detailed computational aspects. Applications in the framework of the SEMIFAR (semiparametric fractional autoregressive) model (Beran, 1999) illustrate the practical usefulness of the methods described here.Nonparametric regression, FARIMA error processes, bandwidth selection, iterative plug-in, SEMIFAR model
Filtered Log-periodogram Regression of long memory processes
Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on Ė d is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a simple family of filters. The essential improvement is based on a binary decision that is asymptotically correct with probability one. The idea is closely related to the well known technique of pre-whitening.
Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors
Optimal rate of convergence, nonparametric regression, long memory, antipersistence.
A nonparametric regression cross spectrum for multivariate time series
We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these quantities is based on wavelet thresholding. The method is illustrated by a simulated example and a three-dimensional time series consisting of ECG, blood pressure and cardiac stroke volume measurements.Nonparametric trend estimation, cross spectrum, wavelets, regression spectrum, phase, threshold estimator
Estimation of a nonparametric regression spectrum for multivariate time series
Estimation of a nonparametric regression spectrum based on the periodogram is considered. Neither trend estimation nor smoothing of the periodogram are required. Alternatively, for cases where spectral estimation of phase shifts fails and the shift does not depend on frequency, a time domain estimator of the lag-shift is defined. Asymptotic properties of the frequency and time domain estimators are derived. Simulations and a data example illustrate the methods.Periodogram, cross spectrum, regression spectrum, phase, wavelets.
Fitting long-memory models by generalized linear regression
SUMMARY There is an increasing awareness of the importance of long-memory models in statistical applications. If long memory is present, it has to be taken into account in order to obtain reliable tests and confidence intervals. One obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software. Here we propose a simple but flexible class of parametric models, which can be used to model such behaviour. We demonstrate that these models can be fitted by generalized linear regression. Standard statistical software packages can be used. A data example is discusse
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