Asymptotics of the sample mean and sample covariance of long-range-dependent series

2004 ◽  
Vol 41 (A) ◽  
pp. 383-392
Author(s):  
Wen Dai
Keyword(s):  
Time Series ◽  
Long Range ◽  
Law Of Large Numbers ◽  
Stationary Time Series ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Sample Mean ◽  
Large Numbers ◽  
Sample Covariance ◽  
Dependent Series

An asymptotic distribution is given for the partial sums of a stationary time-series with long-range dependence. The law of large numbers for the sample covariance of the series is also derived. The results differ from those given elsewhere in relaxing the assumption of the independence of the innovations of the series.

Asymptotics of the sample mean and sample covariance of long-range-dependent series

2004 ◽  
Vol 41 (A) ◽  
pp. 383-392
Author(s):  
Wen Dai
Keyword(s):  
Time Series ◽  
Long Range ◽  
Law Of Large Numbers ◽  
Stationary Time Series ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Sample Mean ◽  
Large Numbers ◽  
Sample Covariance ◽  
Dependent Series

An asymptotic distribution is given for the partial sums of a stationary time-series with long-range dependence. The law of large numbers for the sample covariance of the series is also derived. The results differ from those given elsewhere in relaxing the assumption of the independence of the innovations of the series.

scholarly journals Detecting long-range dependence in non-stationary time series

2017 ◽  
Vol 11 (1) ◽  
pp. 1600-1659 ◽  
Author(s):  
Holger Dette ◽  
Philip Preuss ◽  
Kemal Sen
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Stationary Time

scholarly journals Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data

2016 ◽  
Vol 48 (2) ◽  
pp. 349-368
Author(s):  
Michael A. Kouritzin ◽  
Samira Sadeghi
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Law Of Large Numbers ◽  
Nonlinear Function ◽  
Dependent Data ◽  
Long Range Dependence ◽  
Linear Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Heavy Tailed

Abstract The Marcinkiewicz strong law, limn→∞(1 / n1/p)∑k=1n(Dk - D) = 0 almost surely with p ∈ (1, 2), is studied for outer products Dk = {XkX̅kT}, where {Xk} and {X̅k} are both two-sided (multivariate) linear processes (with coefficient matrices (Cl), (C̅l) and independent and identically distributed zero-mean innovations {Ξ} and {Ξ̅}). Matrix sequences Cl and C ̅l can decay slowly enough (as |l| → ∞) that {Xk,X ̅k} have long-range dependence, while {Dk} can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {Dk} are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy tails or the long-range dependence, but not the combination. The main result is applied to obtain a Marcinkiewicz strong law of large numbers for stochastic approximation, nonlinear function forms, and autocovariances.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (04) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

scholarly journals Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Entropy ◽  
2016 ◽  
Vol 18 (1) ◽  
pp. 23 ◽  
Author(s):  
Qing Li ◽  
Steven Liang ◽  
Jianguo Yang ◽  
Beizhi Li
Keyword(s):  
Time Series ◽  
Long Range ◽  
Chaotic Time Series ◽  
Long Range Dependence ◽  
Vibration Intensity ◽  
Bearing Vibration

Representative Time Series Fractal Analysis of the Traffic Flows of a Dedicated High-Speed Link

2021 ◽  
Author(s):  
Ginno Millan ◽  
manuel vargas ◽  
Guillermo Fuertes
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Long Range Dependence ◽  
Traffic Flows ◽  
Speed Computer

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link exhibited fractal behavior since the Hurst exponent was in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between -0.5, 0. Based on these results, it is ideal to characterize both the singularities of the fractal traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyzes, the fact that the traffic flows of current computer networks exhibited fractal behavior with a long-range dependence was reaffirmed.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

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