Change-of-variance problem for linear processes with long memory

2006 ◽  
Vol 47 (2) ◽  
pp. 279-298 ◽  
Author(s):  
Lihong Wang ◽  
Jinde Wang
Keyword(s):  
Long Memory ◽  
Linear Processes

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.

scholarly journals On functional limits of short- and long-memory linear processes with GARCH(1,1) noises

2015 ◽  
Vol 125 (2) ◽  
pp. 482-512 ◽  
Author(s):  
Rong-Mao Zhang ◽  
Chor-yiu (CY) Sin ◽  
Shiqing Ling
Keyword(s):  
Long Memory ◽  
Linear Processes

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 ASYMPTOTIC NORMALITY FOR WEIGHTED SUMS OF LINEAR PROCESSES

2013 ◽  
Vol 30 (1) ◽  
pp. 252-284 ◽  
Author(s):  
Karim M. Abadir ◽  
Walter Distaso ◽  
Liudas Giraitis ◽  
Hira L. Koul
Keyword(s):  
Asymptotic Normality ◽  
Long Memory ◽  
Moving Average ◽  
Regression Function ◽  
Linear Process ◽  
Triangular Array ◽  
Weighted Sums ◽  
Martingale Differences ◽  
Linear Processes ◽  
Arch Models

We establish asymptotic normality of weighted sums of linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and innovations. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular, they are applicable to GARCH and ARCH(∞) models and to their squares. They are also useful in deriving asymptotic normality of kernel-type estimators of a nonparametric regression function with short or long memory moving average errors.

scholarly journals Randomized pivots for means of short and long memory linear processes

Bernoulli ◽  
2017 ◽  
Vol 23 (4A) ◽  
pp. 2558-2586 ◽  
Author(s):  
Miklós Csörgő ◽  
Masoud M. Nasari ◽  
Mohamedou Ould-Haye
Keyword(s):  
Long Memory ◽  
Linear Processes

scholarly journals ASYMPTOTIC PROPERTIES OF SELF-NORMALIZED LINEAR PROCESSES WITH LONG MEMORY

2011 ◽  
Vol 28 (3) ◽  
pp. 548-569 ◽  
Author(s):  
Magda Peligrad ◽  
Hailin Sang
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Heavy Tails ◽  
Asymptotic Properties ◽  
The Self ◽  
Linear Processes ◽  
Economic Applications ◽  
Memory Time

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic applications where often the linear processes have long memory, and the innovations have heavy tails.

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