scholarly journals A note on joint functional convergence of partial sum and maxima for linear processes

2018 ◽  
Vol 138 ◽  
pp. 42-46 ◽  
Author(s):  
Danijel Krizmanić
Keyword(s):  
Linear Processes ◽  
Partial Sum ◽  
Functional Convergence

scholarly journals THE INVARIANCE PRINCIPLE FOR LINEAR PROCESSES WITH APPLICATIONS

2002 ◽  
Vol 18 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Qiying Wang ◽  
Yan-Xia Lin ◽  
Chandra M. Gulati
Keyword(s):  
Wiener Process ◽  
Invariance Principle ◽  
Random Variables ◽  
Linear Process ◽  
Standard Wiener Process ◽  
Test Statistic ◽  
Linear Processes ◽  
Partial Sum ◽  
Unit Root Testing ◽  
Partial Sum Process

Let Xt be a linear process defined by Xt = [sum ]k=0∞ ψkεt−k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the Xt converging to a standard Wiener process on [0,1], are presented in this paper. In the first result, we assume that the innovations εk are independent and identically distributed random variables but do not restrict [sum ]k=0∞ |ψk| < ∞. We note that, for the partial sum process of the Xt converging to a standard Wiener process, the condition [sum ]k=0∞ |ψk| < ∞ or stronger conditions are commonly used in previous research. The second result is for the situation where the innovations εk form a martingale difference sequence. For this result, the commonly used assumption of equal variance of the innovations εk is weakened. We apply these general results to unit root testing. It turns out that the limit distributions of the Dickey–Fuller test statistic and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test statistic still hold for the more general models under very weak conditions.

scholarly journals Functional Convergence of Linear Processes with Heavy-Tailed Innovations

2014 ◽  
Vol 29 (2) ◽  
pp. 491-526 ◽  
Author(s):  
Raluca Balan ◽  
Adam Jakubowski ◽  
Sana Louhichi
Keyword(s):  
Linear Processes ◽  
Functional Convergence ◽  
Heavy Tailed

Efficient Algorithms for the Partial Sum Dispersion Problem

2020 ◽  
Vol E103.A (10) ◽  
pp. 1206-1210
Author(s):  
Toshihiro AKAGI ◽  
Tetsuya ARAKI ◽  
Shin-ichi NAKANO
Keyword(s):  
Efficient Algorithms ◽  
Partial Sum ◽  
Dispersion Problem

The structure of non-linear processes

Tellus ◽  
1973 ◽  
Vol 25 (6) ◽  
pp. 536-544 ◽  
Author(s):  
A. Quinet
Keyword(s):  
Linear Processes ◽  
Non Linear

Direct digital control of linear processes subject to random disturbances

AIChE Journal ◽  
1972 ◽  
Vol 18 (4) ◽  
pp. 846-849
Author(s):  
Richard E. Kloubec ◽  
Henry C. Lim
Keyword(s):  
Digital Control ◽  
Linear Processes ◽  
Random Disturbances ◽  
Direct Digital Control

scholarly journals Applications of soft computing models for predicting sea surface temperature: a comprehensive review and assessment

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Masoud Haghbin ◽  
Ahmad Sharafati ◽  
Davide Motta ◽  
Nadhir Al-Ansari ◽  
Mohamadreza Hosseinian Moghadam Noghani
Keyword(s):  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Soft Computing ◽  
Sea Surface ◽  
Linear Processes ◽  
Comprehensive Review ◽  
Droughts And Floods ◽  
Input Variables ◽  
And Performance ◽  
Computing Models

AbstractThe application of soft computing (SC) models for predicting environmental variables is widely gaining popularity, because of their capability to describe complex non-linear processes. The sea surface temperature (SST) is a key quantity in the analysis of sea and ocean systems, due to its relation with water quality, organisms, and hydrological events such as droughts and floods. This paper provides a comprehensive review of the SC model applications for estimating SST over the last two decades. Types of model (based on artificial neural networks, fuzzy logic, or other SC techniques), input variables, data sources, and performance indices are discussed. Existing trends of research in this field are identified, and possible directions for future investigation are suggested.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

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