Results 1  10
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55
On adaptive estimation in nonstationary ARMA models with GARCH errors
 Ann. Statist
, 2003
"... This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the loglikelihood ratio for the model is obtained. It is show ..."
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Cited by 46 (34 self)
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This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the loglikelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. Adaptivity is discussed and it is found that the parameters in the model are generally not adaptively estimable if the density of the rescaled error is asymmetric. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a class of defined Mνestimators. It is shown that such efficient estimators can be constructed when the density is known. Using the kernel estimator for the score function, adaptive estimators are constructed when the density of the rescaled error is symmetric, and it is shown that the adaptive procedure for the parameters in the conditional mean part uses the full sample without splitting. These estimators are demonstrated to be
Root n Consistent and Optimal Density Estimators for Moving Average Processes
"... The marginal density of a first order moving average process can be written as convolution of two innovation densities. Saavedra and Cao (2000) propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain ..."
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Cited by 21 (17 self)
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The marginal density of a first order moving average process can be written as convolution of two innovation densities. Saavedra and Cao (2000) propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain that for an appropriate choice of bandwidth the variance of their estimator decreases at the rate 1/n. Their estimator can be interpreted as a specific Ustatistic. We suggest a slightly simpli ed Ustatistic as estimator of the marginal density, prove that it is asymptotically normal at the same rate, and describe the asymptotic variance explicitly. We show that the estimator is asymptotically efficient if no structural assumptions are made on the innovation density. For innovation densities known to have mean zero or to be symmetric, we describe improvements of our estimator which are again asymptotically efficient.
RANKBASED OPTIMAL TESTS OF THE ADEQUACY OF AN ELLIPTIC VARMA MODEL
, 2002
"... We are deriving optimal rankbased tests for the adequacy of a vector autoregressivemoving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudoMahalanobis distances and on normed residuals computed from Tyler’s [Ann. Statist. 15 (1987) ..."
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Cited by 21 (17 self)
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We are deriving optimal rankbased tests for the adequacy of a vector autoregressivemoving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudoMahalanobis distances and on normed residuals computed from Tyler’s [Ann. Statist. 15 (1987) 234–251] scatter matrix; they generalize the univariate signed rank procedures proposed by Hallin and Puri [J. Multivariate Anal. 39 (1991) 1–29]. Two types of optimality properties are considered, both in the local and asymptotic sense, a la Le Cam: (a) (fixedscore procedures) local asymptotic minimaxity at selected radial densities, and (b) (estimatedscore procedures) local asymptotic minimaxity uniform over a class F of radial densities. Contrary to their classical counterparts, based on crosscovariance matrices, these tests remain valid under arbitrary elliptically symmetric innovation densities, including those with infinite variance and heavytails. We show that the AREs of our fixedscore
Weighted ResidualBased Density Estimators For Nonlinear Autoregressive Models
"... This paper considers residualbased and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted L1norms. These estimators ..."
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Cited by 18 (13 self)
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This paper considers residualbased and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted L1norms. These estimators give rise to smoothed and weighted empirical distribution functions and moments. It is shown that the latter are efficient if an efficient estimator for the autoregression parameter is used to construct the residuals.
Estimating the Innovation Distribution in Nonlinear Autoregressive Models
 Department of Mathematics, University of Siegen. http://www.math.unisiegen.de/statistik/wefelmeyer.html
"... The usual estimator for the expectation of a function under the innovation distribution of a nonlinear autoregressive model is the empirical estimator based on estimated innovations. It can be improved by exploiting that the innovation distribution has mean zero. We show that the resulting estimator ..."
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Cited by 17 (17 self)
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The usual estimator for the expectation of a function under the innovation distribution of a nonlinear autoregressive model is the empirical estimator based on estimated innovations. It can be improved by exploiting that the innovation distribution has mean zero. We show that the resulting estimator is efficient if the innovations are estimated with an efficient estimator for the autoregression parameter. Efficiency of this estimator is necessary except when the expectation of the function can be estimated adaptively. Analogous results hold for heteroscedastic models.
Semiparametric Duration Models
, 2001
"... In this paper we consider semiparametric duration models and efficient estimation of the parameters in a noni.i.d. environment. In contrast to classical time series models where innovations are assumed to be i.i.d., we show that, for example in the oftenused Autoregressive Conditional Duration (AC ..."
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Cited by 13 (2 self)
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In this paper we consider semiparametric duration models and efficient estimation of the parameters in a noni.i.d. environment. In contrast to classical time series models where innovations are assumed to be i.i.d., we show that, for example in the oftenused Autoregressive Conditional Duration (ACD) model, the assumption of independent innovations is too restrictive to describe financial durations accurately. Therefore, we consider semiparametric extensions of the standard specification that allow for arbitrary kinds of dependencies between the innovations. The exact nonparametric specification of these dependencies determines the flexibility of the semiparametric model. We calculate semiparametric efficiency bounds for the ACD parameters, discuss the construction of efficient estimators, and study the efficiency loss of the exponential pseudolikelihood procedure. This efficiency loss proves to be sizeable in applications. For durations observed on the Paris Bourse for the Alcatel stock in July and August 1996, the proposed semiparametric procedures clearly outperform pseudolikelihood procedures. We analyze these efficiency gains using a simulation study which confirms that, at least at the Paris Bourse, dependencies among rescaled durations can be exploited.
Efficiency improvements in inference on stationary and nonstationary fractional time series
 ANNALS OF STATISTICS
, 2005
"... We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing ..."
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Cited by 12 (7 self)
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We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing descriptions of trending behavior. The stationary input to the stochastic component has parametric autocorrelation, but innovation with distribution of unknown form. The model is thus semiparametric, and we develop estimates of the parametric component which are asymptotically normal and achieve an Mestimation efficiency bound, equal to that found in work using an adaptive LAM/LAN approach. A major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies. This is relevant also when the innovation density is parameterized, and we provide a result for that case also. Our semiparametric estimates employ nonparametric series estimation, which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models; our work thus also contributes to methods and theory for nonfractional time series models, such as autoregressive moving averages. A Monte Carlo study of finite sample performance of the semiparametric estimates is included.
Estimating invariant laws of linear processes by Ustatistics
"... Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional... ..."
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Cited by 11 (10 self)
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Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional...
Autoregressive Conditional Duration (ACD) Models in Finance: A Survey of the Theoretical and Empirical Literature
, 2006
"... ..."
Semiparametric multivariate volatility models
 Econometric Theory
, 2007
"... Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle ..."
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Cited by 10 (2 self)
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Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle