On convergence of moving average series of martingale differences fields taking values in Banach spaces

2017 ◽  
Vol 47 (22) ◽  
pp. 5590-5603 ◽  
Author(s):  
Ta Cong Son ◽  
Dang Hung Thang ◽  
Le Van Dung
Keyword(s):  
Banach Spaces ◽  
Moving Average ◽  
Martingale Differences

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 Complete Convergence for Moving Average Process of Martingale Differences

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Martingale Differences ◽  
Moment Convergence ◽  
Moving Process

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

2000 ◽  
Vol 16 (1) ◽  
pp. 3-22 ◽  
Author(s):  
Liudas Giraitis ◽  
Piotr Kokoszka ◽  
Remigijus Leipus
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Broad Class ◽  
Moving Average ◽  
Sufficient Conditions ◽  
Dependence Structure ◽  
Martingale Differences ◽  
Arch Models ◽  
Moving Average Representation

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

Automatic Identification of Autoregressive Integrated Moving Average Time Series

1982 ◽  
Vol 14 (3) ◽  
pp. 156-166 ◽  
Author(s):  
Chin-Sheng Alan Kang ◽  
David D. Bedworth ◽  
Dwayne A. Rollier
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Automatic Identification ◽  
Autoregressive Integrated Moving Average

Smoothing Facilitates the Detection of Coupled Responses in Psychophysiological Time Series

2000 ◽  
Vol 14 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Joni Kettunen ◽  
Niklas Ravaja ◽  
Liisa Keltikangas-Järvinen
Keyword(s):  
Time Series ◽  
Type I Error ◽  
Electrodermal Activity ◽  
Moving Average ◽  
Type I ◽  
Facial Electromyography ◽  
Response Characteristics ◽  
Smoothing Methods ◽  
Response Systems ◽  
Different Response

Abstract We examined the use of smoothing to enhance the detection of response coupling from the activity of different response systems. Three different types of moving average smoothers were applied to both simulated interbeat interval (IBI) and electrodermal activity (EDA) time series and to empirical IBI, EDA, and facial electromyography time series. The results indicated that progressive smoothing increased the efficiency of the detection of response coupling but did not increase the probability of Type I error. The power of the smoothing methods depended on the response characteristics. The benefits and use of the smoothing methods to extract information from psychophysiological time series are discussed.

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