Limit theorems for long-memory flows on Wiener chaos

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1473-1503 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Memory ◽  
Limit Theorems ◽  
Wiener Chaos

scholarly journals Covariances Estimation for Long-Memory Processes

2010 ◽  
Vol 42 (1) ◽  
pp. 137-157 ◽  
Author(s):  
Wei Biao Wu ◽  
Yinxiao Huang ◽  
Wei Zheng
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Long Memory ◽  
Limit Theorems ◽  
Limiting Distribution ◽  
Linear Processes ◽  
Long Memory Processes ◽  
Noncentral Limit Theorems ◽  
Dependence Properties

For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

Spectral Analysis for Bivariate Time Series with Long Memory

1996 ◽  
Vol 12 (5) ◽  
pp. 773-792 ◽  
Author(s):  
J. Hidalgo
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Long Memory ◽  
Limit Theorems ◽  
Stationary Process ◽  
Absolute Summability ◽  
Spectral Density Matrix ◽  
Mixing Coefficients ◽  
Long Memory Processes

This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.

scholarly journals Covariances Estimation for Long-Memory Processes

2010 ◽  
Vol 42 (01) ◽  
pp. 137-157 ◽  
Author(s):  
Wei Biao Wu ◽  
Yinxiao Huang ◽  
Wei Zheng
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Long Memory ◽  
Limit Theorems ◽  
Limiting Distribution ◽  
Linear Processes ◽  
Long Memory Processes ◽  
Noncentral Limit Theorems ◽  
Dependence Properties

For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

scholarly journals QUANTILOGRAMS UNDER STRONG DEPENDENCE

2019 ◽  
Vol 36 (3) ◽  
pp. 457-487 ◽  
Author(s):  
Ji Hyung Lee ◽  
Oliver Linton ◽  
Yoon-Jae Whang
Keyword(s):  
Confidence Interval ◽  
Central Limit ◽  
Long Memory ◽  
Limit Theorems ◽  
Strong Dependence ◽  
Nuisance Parameters ◽  
Block Bootstrap ◽  
Limit Theory ◽  
Moving Block Bootstrap ◽  
Predictive Relations

We develop the limit theory of the quantilogram and cross-quantilogram under long memory. We establish the sub-root-n central limit theorems for quantilograms that depend on nuisance parameters. We propose a moving block bootstrap (MBB) procedure for inference and establish its consistency, thereby enabling a consistent confidence interval construction for the quantilograms. The newly developed reduction principles for the quantilograms serve as the main technical devices used to derive the asymptotics and establish the validity of MBB. We report some simulation evidence that our methods work satisfactorily. We apply our method to quantile predictive relations between financial returns and long-memory predictors.

scholarly journals The impact of the diagonals of polynomial forms on limit theorems with long memory

Bernoulli ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 710-742 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Memory ◽  
Limit Theorems ◽  
The Impact

Limit theorems and price changes in financial markets

1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Limit Theorems ◽  
Price Changes
Sign in / Sign up

Export Citation Format

Share Document