scholarly journals Confidence intervals with higher accuracy for short and long-memory linear processes

2021 ◽  
Author(s):  
Masoud M. Nasari ◽  
Mohamedou Ould-Haye
Keyword(s):  
Confidence Intervals ◽  
Long Memory ◽  
Linear Processes

scholarly journals Variability and Confidence Intervals for the Mean of Climate Data with Short- and Long-Range Dependence

2018 ◽  
Vol 31 (15) ◽  
pp. 6135-6156 ◽  
Author(s):  
Matthew C. Bowers ◽  
Wen-wen Tung
Keyword(s):  
Confidence Intervals ◽  
Long Range ◽  
Long Memory ◽  
Long Range Dependence ◽  
Climate Data ◽  
Temperature State ◽  
Correlation Structures ◽  
The Mean ◽  
Error Bars ◽  
Mean State

This paper presents an adaptive procedure for estimating the variability and determining error bars as confidence intervals for climate mean states by accounting for both short- and long-range dependence. While the prevailing methods for quantifying the variability of climate means account for short-range dependence, they ignore long memory, which is demonstrated to lead to underestimated variability and hence artificially narrow confidence intervals. To capture both short- and long-range correlation structures, climate data are modeled as fractionally integrated autoregressive moving-average processes. The preferred model can be selected adaptively via an information criterion and a diagnostic visualization, and the estimated variability of the climate mean state can be computed directly from the chosen model. The procedure was demonstrated by determining error bars for four 30-yr means of surface temperatures observed at Potsdam, Germany, from 1896 to 2015. These error bars are roughly twice the width as those obtained using prevailing methods, which disregard long memory, leading to a substantive reinterpretation of differences among mean states of this particular dataset. Despite their increased width, the new error bars still suggest that a significant increase occurred in the mean temperature state of Potsdam from the 1896–1925 period to the most recent period, 1986–2015. The new wider error bars, therefore, communicate greater uncertainty in the mean state yet present even stronger evidence of a significant temperature increase. These results corroborate a need for more meticulous consideration of the correlation structures of climate data—especially of their long-memory properties—in assessing the variability and determining confidence intervals for their mean states.

scholarly journals Confidence intervals for long memory regressions

2008 ◽  
Vol 78 (13) ◽  
pp. 1894-1902 ◽  
Author(s):  
Kyungduk Ko ◽  
Jaechoul Lee ◽  
Robert Lund
Keyword(s):  
Confidence Intervals ◽  
Long Memory

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

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 (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

Bootstrap approaches for estimation and confidence intervals of long memory processes

2010 ◽  
Vol 80 (9) ◽  
pp. 959-978
Author(s):  
Luisa Bisaglia ◽  
Silvano Bordignon ◽  
Nedda Cecchinato
Keyword(s):  
Confidence Intervals ◽  
Long Memory ◽  
Memory Processes ◽  
Long Memory Processes
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