Fitting Time Series with Heavy Tails and Strong Time Dependence
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-021-05324-3
Abstract: Earlier, a model of a time series with heavy tails constructed from a Gaussian time series was developed. In the present paper, the reverse problem is considered: an estimator of the copula function is built;… read more here.
Keywords: time; heavy tails; series heavy; time series ... See more keywords
Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails
Sign Up to like & getrecommendations! Published in 2019 at "Statistical Inference for Stochastic Processes"
DOI: 10.1007/s11203-020-09210-8
Abstract: We consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed continuously on a long time interval [0, … read more here.
Keywords: process heavy; heavy tails; ornstein uhlenbeck; process ... See more keywords
Heavy tails for an alternative stochastic perpetuity model
Sign Up to like & getrecommendations! Published in 2019 at "Stochastic Processes and their Applications"
DOI: 10.1016/j.spa.2018.12.008
Abstract: Abstract In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We… read more here.
Keywords: perpetuity; perpetuity model; heavy tails; alternative stochastic ... See more keywords
Hausdorff dimension, heavy tails, and generalization in neural networks
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/ac3ae7
Abstract: Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge. While modeling the trajectories of SGD via… read more here.
Keywords: hausdorff dimension; neural networks; heavy tails; generalization ... See more keywords
Linear Regression for Heavy Tails
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DOI: 10.3390/risks6030093
Abstract: There exist several estimators of the regression line in the simple linear regression: Least Squares, Least Absolute Deviation, Right Median, Theil–Sen, Weighted Balance, and Least Trimmed Squares. Their performance for heavy tails is compared below… read more here.
Keywords: heavy tails; regression heavy; distribution; linear regression ... See more keywords