Limit theory for moving averages of random variables with regularly varying tail probabilities
From MaRDI portal
Publication:1056976
DOI10.1214/aop/1176993074zbMath0562.60026OpenAlexW2003695184MaRDI QIDQ1056976
Richard A. Davis, Sidney I. Resnick
Publication date: 1985
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1176993074
Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)
Related Items
The Extremal Dependence Measure and Asymptotic Independence ⋮ Automated Estimation of Heavy-Tailed Vector Error Correction Models ⋮ A Gini Autocovariance Function for Time Series Modelling ⋮ Limit Theory for High Frequency Sampled MCARMA Models ⋮ Regular Variation of Infinite Series of Processes with Random Coefficients ⋮ Noncausal Autoregressive Model in Application to Bitcoin/USD Exchange Rates ⋮ Asymptotics of the sample mean and sample covariance of long-range-dependent series ⋮ Modelling of extremal events in insurance and finance ⋮ Extremes of autoregressive threshold processes ⋮ Large sample theory for statistics of stable moving averages ⋮ Inference for the VEC(1) model with a heavy-tailed linear process errors* ⋮ Inference in Heavy-Tailed Nonstationary Multivariate Time Series ⋮ Large deviations of \(\ell^p\)-blocks of regularly varying time series and applications to cluster inference ⋮ Some variations on the extremal index ⋮ M-ESTIMATION FOR A SPATIAL UNILATERAL AUTOREGRESSIVE MODEL WITH INFINITE VARIANCE INNOVATIONS ⋮ RATE OF CONVERGENCE OF CENTRED ESTIMATES OF AUTOREGRESSIVE PARAMETERS FOR INFINITE VARIANCE AUTOREGRESSIONS ⋮ UNIT ROOT INFERENCE FOR NON-STATIONARY LINEAR PROCESSES DRIVEN BY INFINITE VARIANCE INNOVATIONS ⋮ Subsampling inference for the autocovariances and autocorrelations of long‐memory heavy‐ tailed linear time series ⋮ ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE ⋮ Limit Theorems for Long-Memory Stochastic Volatility Models with Infinite Variance: Partial Sums and Sample Covariances ⋮ TIME SERIES REGRESSION ON INTEGRATED CONTINUOUS-TIME PROCESSES WITH HEAVY AND LIGHT TAILS ⋮ Unnamed Item ⋮ A method for fitting stable autoregressive models using the autocovariation function ⋮ A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares ⋮ Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series ⋮ Stable random fields, point processes and large deviations ⋮ MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES ⋮ Option pricing for infinite variance data ⋮ Extremes of regularly varying Lévy-driven mixed moving average processes ⋮ EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS ⋮ On the estimation of the heavy-tail exponent in time series using the max-spectrum ⋮ Limit Theorems for Moving Averages with Random Coefficients and Heavy-Tailed Noise ⋮ UNIT ROOT TESTS WITH INFINITE VARIANCE ERRORS ⋮ Strong orthogonal decompositions and non-linear impulse response functions for infinite-variance processes ⋮ Hidden regular variation of moving average processes with heavy-tailed innovations ⋮ Estimation for non-negative time series with heavy-tail innovations ⋮ Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors ⋮ Weighted quantile regression for AR model with infinite variance errors ⋮ The supremum of a negative drift random walk with dependent heavy-tailed steps. ⋮ On some estimates based on sample behavior near high level excursions ⋮ Growth rates of sample covariances of stationary symmetric \(\alpha \)-stable processes associated with null recurrent Markov chains ⋮ Whittle parameter estimation for vector ARMA models with heavy-tailed noises ⋮ Extreme value theory for suprema of random variables with regularly varying tail probabilities ⋮ An invariance principle for sums and record times of regularly varying stationary sequences ⋮ Functional convergence of linear processes with heavy-tailed innovations ⋮ On the extremes of a class of non-linear processes with heavy tailed innovations ⋮ Bivariate statistical analysis of TCP-flow sizes and durations ⋮ Weighted sums of i.i.d. random variables attracted to integrals of stable processes ⋮ Limit theorems for stable processes with application to spectral density estimation ⋮ Sieve-based inference for infinite-variance linear processes ⋮ Limit theorems for linear random fields with innovations in the domain of attraction of a stable law ⋮ Limit theory for bilinear processes with heavy-tailed noise ⋮ A large deviations approach to limit theory for heavy-tailed time series ⋮ On the characterization of certain point processes ⋮ Periodic moving averages of random variables with regularly varying tails ⋮ Maximum likelihood estimation for \(\alpha \)-stable autoregressive processes ⋮ Extreme value theory for a class of nonstationary time series with applications ⋮ Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution ⋮ Fractional ARIMA with stable innovations ⋮ Extreme value theory for dependent sequences via the Stein-Chen method of Poisson approximation ⋮ Strong approximation for cross-covariances of linear variables with long-range dependence ⋮ On almost sure limit theorems for heavy-tailed products of long-range dependent linear processes ⋮ Moment-based tail index estimation ⋮ The integrated periodogram for long-memory processes with finite or infinite variance ⋮ Limit theory of quadratic forms of long-memory linear processes with heavy-tailed GARCH innovations ⋮ An empirical likelihood approach for symmetric \(\alpha\)-stable processes ⋮ A characterization of \(m\)-dependent stationary infinitely divisible sequences with applications to weak convergence ⋮ Trimmed stable AR(1) processes ⋮ Empirical processes for infinite variance autoregressive models ⋮ The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution ⋮ Tail index estimation in the presence of long-memory dynamics ⋮ Extremal dependence measure and extremogram: the regularly varying case ⋮ Limit theory for the largest eigenvalues of sample covariance matrices with heavy-tails ⋮ A limit theorem for moving averages in the \(\alpha\)-stable domain of attraction ⋮ Stochastic volatility models with possible extremal clustering ⋮ Selecting between causal and noncausal models with quantile autoregressions ⋮ The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes ⋮ Modeling of time series arrays by multistep prediction or likelihood methods. ⋮ New tests for unit roots in autoregressive processes with possibly infinite variance errors ⋮ High-level dependence in time series models ⋮ On the properties of the coefficient of determination in regression models with infinite variance variables ⋮ Joint functional convergence of partial sums and maxima for linear processes ⋮ Stationary bubble equilibria in rational expectation models ⋮ Empirical likelihood approach toward discriminant analysis for dynamics of stable processes ⋮ Discrete rough paths and limit theorems ⋮ Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows ⋮ The distribution of the maximum of a first order moving average: the continuous case ⋮ M-estimation for autoregression with infinite variance ⋮ Asymptotics of self-weighted M-estimators for autoregressive models ⋮ On the measurement and treatment of extremes in time series ⋮ A complete convergence theorem for stationary regularly varying multivariate time series ⋮ A note on the normalizing sequences for sums of linear processes in the case of negative memory ⋮ Extreme value theory for space-time processes with heavy-tailed distributions ⋮ Misspecification of noncausal order in autoregressive processes ⋮ Convergence rates in the central limit theorem for means of autoregressive and moving average sequences ⋮ Spectral estimates and stable processes ⋮ Model identification for infinite variance autoregressive processes ⋮ A functional limit theorem for dependent sequences with infinite variance stable limits ⋮ Ergodic theory, abelian groups and point processes induced by stable random fields ⋮ Point processes associated with stationary stable processes ⋮ Whittle estimation in a heavy-tailed GARCH(1,1) model. ⋮ On the extremal behaviour of generalized periodic sub-sampled moving average models with regularly varying tails ⋮ Functional limit theorems for linear processes in the domain of attraction of stable laws ⋮ On the estimation and application of max-stable processes ⋮ Stable limits for sums of dependent infinite variance random variables ⋮ Convergence to Lévy stable processes under some weak dependence conditions ⋮ Topological crackle of heavy-tailed moving average processes ⋮ Time-changed extremal process as a random sup measure ⋮ On functional limits of short- and long-memory linear processes with GARCH(1,1) noises ⋮ The asymptotic behavior of quadratic forms in \(\varphi\)-mixing random variables ⋮ Sample autocovariances of long-memory time series ⋮ Maxima of long memory stationary symmetric \(\alpha\)-stable processes, and self-similar processes with stationary max-increments ⋮ Some aspects of extreme value statistics under serial dependence ⋮ Inference in heavy-tailed vector error correction models ⋮ Inverse problems for regular variation of linear filters, a cancellation property for \(\sigma\)-finite measures and identification of stable laws ⋮ \(\alpha\)-stable limit theorems for sums of dependent random vectors ⋮ Robust causality test of infinite variance processes ⋮ Estimating the parameters of rare events ⋮ The Durbin-Watson ratio under infinite-variance errors ⋮ Gauss-Newton and M-estimation for ARMA processes with infinite variance ⋮ Consistency for least squares regression estimators with infinite variance data ⋮ Extremal dependence measure for functional data ⋮ Principal components analysis of regularly varying functions ⋮ How misleading can sample ACFs of stable MAs be? (Very!) ⋮ Gaussian limit fields for the integrated periodogram ⋮ Extreme value theory for moving average processes with light-tailed innovations ⋮ Convergence of point processes with weakly dependent points ⋮ Cointegrated processes with infinite variance innovations ⋮ A simple robust estimation method for the thickness of heavy tails ⋮ Extremes of Volterra series expansions with heavy-tailed innovations ⋮ Uniform convergence of sample second moments of families of time series arrays. ⋮ Principal component analysis of infinite variance functional data ⋮ Discrete time parametric models with long memory and infinite variance ⋮ Limiting distribution of sums of nonnegative stationary random variables ⋮ More limit theory for the sample correlation function of moving averages ⋮ Diagnostic checking in linear processes with infinite variance ⋮ Subexponentiality of the product of independent random variables ⋮ Functional weak convergence of partial maxima processes