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Search: Peter J. Brockwell
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1.
Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series
Title:
Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series
Author:
Qiwei Yao
;
Peter J. Brockwell
Qiwei Yao
;
Peter J. Brockwell
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Description:
We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive movingaverage (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130145] via the asymptotic properties of a Whittle's estima...
We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive movingaverage (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130145] via the asymptotic properties of a Whittle's estimator. This also paves the way to establish similar results for spatial processes presented in the followup article by Yao and
Brockwell
[Bernoulli (2006) in press]. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.
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Document Type:
article
URL:
http://www.blackwellsynergy.com/doi/abs/10.1111/j.14679892.2006.00492.x
http://www.blackwellsynergy.com/doi/abs/10.1111/j.14679892.2006.00492.x
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RePEc: Research Papers in Economics
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2.
Strictly stationary solutions of autoregressive moving average equations
Title:
Strictly stationary solutions of autoregressive moving average equations
Author:
Peter J. Brockwell
;
Alexander Lindner
Peter J. Brockwell
;
Alexander Lindner
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Description:
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive moving average process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made. Copyright 2010, Oxford University Press.
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive moving average process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made. Copyright 2010, Oxford University Press.
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Document Type:
article
URL:
http://hdl.handle.net/10.1093/biomet/asq034
http://hdl.handle.net/10.1093/biomet/asq034
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RePEc: Research Papers in Economics
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3.
Gaussian maximum likelihood estimation for ARMA models I: Times series
Open Access
Title:
Gaussian maximum likelihood estimation for ARMA models I: Times series
Author:
Qiwei Yao
;
Peter J. Brockwell
;
Qiwei Yao
;
Peter J. Brockwell
Qiwei Yao
;
Peter J. Brockwell
;
Qiwei Yao
;
Peter J. Brockwell
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Description:
Gaussian maximum likelihood estimation for ARMA models II: spatial processes Article (Accepted version)
Gaussian maximum likelihood estimation for ARMA models II: spatial processes Article (Accepted version)
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20141220
Source:
http://eprints.lse.ac.uk/5416/1/Gaussian_maximum_likelihood_estimation_for_ARMA_models_IIspatial_processes(LSERO).pdf
http://eprints.lse.ac.uk/5416/1/Gaussian_maximum_likelihood_estimation_for_ARMA_models_IIspatial_processes(LSERO).pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.489.3347
http://eprints.lse.ac.uk/5416/1/Gaussian_maximum_likelihood_estimation_for_ARMA_models_IIspatial...
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.489.3347
http://eprints.lse.ac.uk/5416/1/Gaussian_maximum_likelihood_estimation_for_ARMA_models_IIspatial...
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4.
Autoregressions Generated by the Tent Map
Open Access
Title:
Autoregressions Generated by the Tent Map
Author:
Peter J. Brockwell
Peter J. Brockwell
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Description:
It is wellknown (see e.g. Tong, 1990, Gourieroux, 1997) that if X0 has the uniform distribution function U on [0 � 1], then the sequence of iterates fXn = g(Xn;1)g of the symmetric tent mapg from [0 � 1] onto [0 � 1], is a strictly stationary Markov process with marginal distribution function U. It is also easy to show, using the symmetry of th...
It is wellknown (see e.g. Tong, 1990, Gourieroux, 1997) that if X0 has the uniform distribution function U on [0 � 1], then the sequence of iterates fXn = g(Xn;1)g of the symmetric tent mapg from [0 � 1] onto [0 � 1], is a strictly stationary Markov process with marginal distribution function U. It is also easy to show, using the symmetry of the map, that fXng is white noise. In this note we show that if the symmetric tent map is replaced by askewed tent map, then the sequence fXng is a strictly stationary autoregression of order 1 with coe cient = (2=s) ; 1, where s 2 (1 � 1) is the rightderivative ofthetent map at 0. An AR(1) process with uniform marginal distributions and arbitrary coe cient 2 (;1 � 1) can thus be generated by computing the iterates with s =2= ( +1). For the symmetric map s =2and =0. Keywords: Nonlinear dynamical system, chaos, nonlinear time series, linear prediction.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20101223
Source:
http://wwwm4.ma.tum.de/Papers/Klueppelberg/chaos.pdf
http://wwwm4.ma.tum.de/Papers/Klueppelberg/chaos.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.3803
http://wwwm4.ma.tum.de/Papers/Klueppelberg/chaos.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.3803
http://wwwm4.ma.tum.de/Papers/Klueppelberg/chaos.pdf
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5.
Lévydriven and fractionally integrated ARMA processes with continuous time parameter
Open Access
Title:
Lévydriven and fractionally integrated ARMA processes with continuous time parameter
Author:
Peter J. Brockwell
;
Tina Marquardt
Peter J. Brockwell
;
Tina Marquardt
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Description:
The de nition and properties of Levydriven CARMA (continuoustime ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving Levy process is Brownian motion. The use of more general Levy processes permits the speci cation of CARMA processes with a wide variety ofmarginal distributions which may be asymmetric a...
The de nition and properties of Levydriven CARMA (continuoustime ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving Levy process is Brownian motion. The use of more general Levy processes permits the speci cation of CARMA processes with a wide variety ofmarginal distributions which may be asymmetric and heavier tailed than Gaussian. Nonnegative CARMA processes are of special interest, partly because of the introduction by BarndorNielsen and Shephard (2001) of nonnegativeLevydriven OrnsteinUhlenbeck processes as models for stochastic volatility. Replacing the OrnsteinUhlenbeck process byaLevydriven CARMA process with nonnegative kernel permits the modelling of nonnegative, heavytailed processes with a considerably larger range of autocovariance functions than is possible in the OrnsteinUhlenbeck framework. We also de ne a class of zeromean fractionally integrated Levydriven CARMA processes, obtained by convoluting the CARMA kernel with a kernel corresponding to RiemannLiouville fractional integration, and derive explicit expressions for the kernel and autocovariance functions of these processes. They are longmemory in the sense that their kernel and autocovariance functions decay asymptotically at hyperbolic rates depending on the order of fractional integration. In order to introduce longmemory into nonnegative Levydriven CARMA processes we replace the fractional integration kernel with a closely related absolutely integrable kernel. This gives a class of stationary nonnegative continuoustime Levydriven processes whose autocovariance functions at lag h also converge to zero at asymptotically hyperbolic rates.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20101223
Source:
http://wwwm4.ma.tum.de/pers/
brockwell
/ficarma.pdf
http://wwwm4.ma.tum.de/pers/
brockwell
/ficarma.pdf
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Document Type:
text
Language:
en
Subjects:
continuoustime ARMA process ; Levy process ; stochastic volatility ; long memory ; fractional
continuoustime ARMA process ; Levy process ; stochastic volatility ; long memory ; fractional
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DDC:
519 Probabilities & applied mathematics
(computed)
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4537
http://wwwm4.ma.tum.de/pers/brockwell/ficarma.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4537
http://wwwm4.ma.tum.de/pers/brockwell/ficarma.pdf
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6.
Estimation for Nonnegative Levydriven OrnsteinUhlenbeck Processes
Open Access
Title:
Estimation for Nonnegative Levydriven OrnsteinUhlenbeck Processes
Author:
Peter J. Brockwell
;
Richard A. Davis
Peter J. Brockwell
;
Richard A. Davis
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Description:
Continuoustime autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Levy process constitute a very general class of stationary, nonnegative continuoustime processes. In nancial econometrics a stationary OrnsteinUhlenbeck (or CAR(1)) process, driven by a nondecreasing Levy process, was intro...
Continuoustime autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Levy process constitute a very general class of stationary, nonnegative continuoustime processes. In nancial econometrics a stationary OrnsteinUhlenbeck (or CAR(1)) process, driven by a nondecreasing Levy process, was introduced by BarndorNielsen and Shephard (2001) as a model for stochastic volatility toallow for a wide variety of possible marginal distributions and the possibility of jumps. For such processes we take advantage of the nonnegativity of the increments of the driving Levy process to study the properties of a highly e cient estimation procedure for the parameters when observations are available of the CAR(1) process at uniformly spaced times 0�h�::: �Nh.We also show howto reconstruct the background driving Levy process from a continuously observed realization of the process and use this result to estimate the increments of the Levy process itself when h is small. Asymptotic properties of the coe cient estimator are derived and the results illustrated using a simulated gammadriven OrnsteinUhlenbeck process.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20101223
Source:
http://wwwm4.ma.tum.de/Papers/
brockwell
/LevyOU.pdf
http://wwwm4.ma.tum.de/Papers/
brockwell
/LevyOU.pdf
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Document Type:
text
Language:
en
DDC:
519 Probabilities & applied mathematics
(computed)
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.5075
http://wwwm4.ma.tum.de/Papers/brockwell/LevyOU.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.5075
http://wwwm4.ma.tum.de/Papers/brockwell/LevyOU.pdf
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7.
High frequency sampling of a continuoustime ARMA process
Open Access
Title:
High frequency sampling of a continuoustime ARMA process
Author:
Peter J. Brockwell
;
Vincenzo Ferrazzano
Peter J. Brockwell
;
Vincenzo Ferrazzano
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Description:
Continuoustime autoregressive moving average (CARMA) processes have recently been used widely in the modeling of nonuniformly spaced data and as a tool for dealing with highfrequency data of the form Yn∆, n = 0, 1, 2,., where ∆ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbu...
Continuoustime autoregressive moving average (CARMA) processes have recently been used widely in the modeling of nonuniformly spaced data and as a tool for dealing with highfrequency data of the form Yn∆, n = 0, 1, 2,., where ∆ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process (Yn∆)n∈Z, when ∆ is small and the underlying continuoustime process (Yt)t∈R is a specified CARMA process.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20110330
Source:
http://wwwm4.ma.tum.de/Papers/Ferrazzano/bfkcarma110114.pdf
http://wwwm4.ma.tum.de/Papers/Ferrazzano/bfkcarma110114.pdf
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Document Type:
text
Language:
en
Subjects:
CARMA process ; high frequency data ; discretely sampled process
CARMA process ; high frequency data ; discretely sampled process
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Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.3440
http://wwwm4.ma.tum.de/Papers/Ferrazzano/bfkcarma110114.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.3440
http://wwwm4.ma.tum.de/Papers/Ferrazzano/bfkcarma110114.pdf
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8.
Strictly stationary solutions of autoregressive moving average equations
Open Access
Title:
Strictly stationary solutions of autoregressive moving average equations
Author:
Brockwell, Peter J.
;
Lindner, Alexander
Brockwell, Peter J.
;
Lindner, Alexander
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Description:
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive moving average process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made.
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive moving average process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made.
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Publisher:
Oxford University Press
Year of Publication:
20100901 00:00:00.0
Document Type:
TEXT
Language:
en
Subjects:
Miscellanea
Miscellanea
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Rights:
Copyright (C) 2010, Biometrika Trust
Copyright (C) 2010, Biometrika Trust
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URL:
http://dx.doi.org/10.1093/biomet/asq034
http://biomet.oxfordjournals.org/cgi/content/short/97/3/765
http://dx.doi.org/10.1093/biomet/asq034
http://biomet.oxfordjournals.org/cgi/content/short/97/3/765
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HighWire Press (Stanford University)
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9.
Parametric estimation of the driving L\'evy process of multivariate CARMA processes from discrete observations
Open Access
Title:
Parametric estimation of the driving L\'evy process of multivariate CARMA processes from discrete observations
Author:
Brockwell, Peter J.
;
Schlemm, Eckhard
Brockwell, Peter J.
;
Schlemm, Eckhard
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Description:
We consider the parametric estimation of the driving L\'evy process of a multivariate continuoustime autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,.)$. Beginning with a new state space representation, we develop a method to recover the driving L\'evy process exactly from a continuous record...
We consider the parametric estimation of the driving L\'evy process of a multivariate continuoustime autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,.)$. Beginning with a new state space representation, we develop a method to recover the driving L\'evy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving L\'evy process from discretetime observations of the MCARMA process. We show that, if the sampling interval $h=h_N$ is chosen dependent on $N$, the length of the observation horizon, such that $N h_N$ converges to zero as $N$ tends to infinity, then any suitable generalized method of moments estimator based on this reconstructed sample of unit increments has the same asymptotic distribution as the one based on the true increments, and is, in particular, asymptotically normally distributed. ; Comment: 38 pages, four figures; to appear in Journal of Multivariate Analysis
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Year of Publication:
20120905
Document Type:
text
Subjects:
Mathematics  Probability ; Mathematics  Statistics Theory ; 62F10 ; 60G51 ; 60F05 (Primary) 60E07 ; 60G10 (Secondary)
Mathematics  Probability ; Mathematics  Statistics Theory ; 62F10 ; 60G51 ; 60F05 (Primary) 60E07 ; 60G10 (Secondary)
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DDC:
519 Probabilities & applied mathematics
(computed)
URL:
http://arxiv.org/abs/1209.0952
http://arxiv.org/abs/1209.0952
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ArXiv.org (Cornell University Library)
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10.
Representations of continuoustime ARMA processes
Title:
Representations of continuoustime ARMA processes
Author:
Brockwell, Peter J.
Brockwell, Peter J.
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Description:
Using the kernel representation of a continuoustime Lévydriven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévydriven OrnsteinUhlenbeck processes employed by BarndorffNielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévydr...
Using the kernel representation of a continuoustime Lévydriven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévydriven OrnsteinUhlenbeck processes employed by BarndorffNielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévydriven continuoustime ARMA processes obtained by a simple modification of the kernel of the continuoustime ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.
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Publisher:
Applied Probability Trust
Year of Publication:
200402
Document Type:
Text
Language:
en
Subjects:
Continuoustime ARMA process ; Lévy process ; stochastic volatility ; long memory ; fractional integration ; 60G10 ; 62P05
Continuoustime ARMA process ; Lévy process ; stochastic volatility ; long memory ; fractional integration ; 60G10 ; 62P05
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Rights:
Copyright 2004 Applied Probability Trust
Copyright 2004 Applied Probability Trust
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Relations:
00219002 ; 14756072
URL:
http://projecteuclid.org/euclid.jap/1082552212
http://projecteuclid.org/euclid.jap/1082552212
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(16) Brockwell, Peter J.
(7) Peter J. Brockwell
(6) The Pennsylvania State University CiteSeerX...
(6) Yao, Qiwei
(5) Davis, Richard A.
(4) Brockwell, Peter J
(3) Brockwell, David J.
(3) Lindner, Alexander
(3) Olmsted, Peter D.
(3) Radford, Sheena E.
(2) Beddard, Godfrey S.
(2) Brockwell, John
(2) Chadraa, Erdenebaatar
(2) Lindner, Alexander M.
(2) Paci, Emanuele
(2) Qiwei Yao
(2) Smith, D. Alastair
(2) Yang, Yu
(1) Alexander Lindner
(1) Annaliisa Laine
(1) BERRY, KENNETH J.
(1) BROCKWELL, PETER J.
(1) Bagnall, David J.
(1) Bauer, Wolfgang D.
(1) Beddard, Godfrey S
(1) Blake, Anthony W
(1) Blake, Anthony W.
(1) Broadhurst, Linda M.
(1) Brockwell, David J
(1) Carroll, Bernard J.
(1) Chen, Changhua
(1) Clarkson, John
(1) Cline, Daren B. H.
(1) David J. Bagnall
(1) Donahue, Rafe M. J.
(1) Ferrazzano, Vincenzo
(1) Gault, Robert R.
(1) Gresshoff, Peter M.
(1) John Brockwell
(1) Klüppelberg, Claudia
(1) Laine, AnnaLiisa
(1) Linda M. Broadhurst
(1) MIELKE, PAUL W.
(1) Mathews, Anne
(1) Olmsted, Peter D
(1) Peter H. Thrall
(1) Radford, Sheena E
(1) Richard A. Davis
(1) Schlemm, Eckhard
(1) Smith, D Alastair
(1) Thrall, Peter H.
(1) Tina Marquardt
(1) Trindade, A. Alexandre
(1) Trinick, John
(1) Vincenzo Ferrazzano
(1) Vollenbroeker, Bernd
(1) WILLIAMS, JAMES S.
(1) West, Dan K.
(1) West, Daniel K.
(1) Zinober, Rebecca C
(1) Zinober, Rebecca C.
Author:
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(3) ha statistics
(3) mathematics probability
(3) mathematics statistics theory
(2) 60g10
(2) continuous time arma process
(2) levy process
(2) long memory
(2) proteins
(2) research article
(2) stochastic volatility
(1) 60f05 primary 60e07
(1) 60g10 secondary
(1) 60g51
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(1) accelerated communication
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(1) c23
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(1) ddc 510
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(1) gaussian maximum likelihood estimator
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(1) legume rhizobium symbiosis
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(1) martingale difference
(1) mathematics spectral theory
(1) miscellanea
(1) nitrate
(1) ornstein uhlenbeck process
(1) sampled process
(1) sonderforschungsbereich 386
(1) stochastic differential equation
(1) symbiotic nitrogen fixation
Subject:
Dewey Decimal Classification (DDC)
(4) Mathematics [51*]
(2) Medicine & health [61*]
(1) Statistics [31*]
(1) Chemistry [54*]
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(17) Open Access
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