scholarly journals A central limit theorem for autoregressive integrated moving average processes

1993 ◽  
Vol 17 (10) ◽  
pp. 3-9 ◽  
Author(s):  
John E. Angus
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Moving Average ◽  
Autoregressive Integrated Moving Average ◽  
Moving Average Processes

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.

scholarly journals A central limit theorem for randomly indexed m-dependent random variables

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 713-717 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Number ◽  
Moving Average ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Average Sequence

In this note, we prove a central limit theorem for the sum of a random number Nn of m-dependent random variables. The sequence Nn and the terms in the sum are not assumed to be independent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.

scholarly journals On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Almost Sure Convergence ◽  
First Passage Percolation ◽  
First Passage ◽  
Percolation Problem ◽  
Vertex Set ◽  
Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

Sign in / Sign up

Export Citation Format

Share Document