Continuous-time fractional ARMA processes

DOI10.1016/0167-7152(94)00015-8zbMath0809.62085OpenAlexW2082480193MaRDI QIDQ1341364

V. Pereyra

Publication date: 9 January 1995

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(94)00015-8

zbMATH Keywords

Laplace transformfractional Brownian motionsimpulse response functionfractional filtercontinuous-time fractional ARMA processes

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15) Sample path properties (60G17)

Related Items (15)

Continuous-time fractional ARMA processes ⋮ Local Hölder exponent estimation for multivariate continuous time processes ⋮ On semilinear stochastic fractional differential equations of Volterra type ⋮ Maximum Likelihood Estimation of Linear Continuous Time Long Memory Processes with Discrete Time Data ⋮ LONG-RANGE DEPENDENCE AND MIXING FOR DISCRETE TIME FRACTIONAL PROCESSES ⋮ On continuous-time autoregressive fractionally integrated moving average processes ⋮ SIMULATION AND ESTIMATION OF LONG MEMORY CONTINUOUS TIME MODELS ⋮ Extending the root-locus method to fractional-order systems ⋮ Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency. ⋮ Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time ⋮ Aggregation of random parameters Ornstein‐Uhlenbeck or AR processes: some convergence results ⋮ Adaptive sampling schemes for density estimation ⋮ Random discretization of stationary continuous time processes ⋮ Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes ⋮ Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes

Cites Work

• Noncentral limit theorems for quadratic forms in random variables having long-range dependence
• Continuous-time fractional ARMA processes
• THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS
• Discrimination between monotonic trends and long-range dependence
• Infinite variance self-similar processes subordinate to a poisson measure
• AN INTRODUCTION TO LONG-MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING
• ON GENERALIZED FRACTIONAL PROCESSES
• Fractional Brownian Motions, Fractional Noises and Applications
• Gaussian sample functions and the Hausdorff dimension of level crossings
• COMPLEX FOURIER--BESSEL TRANSFORMS
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