A law of large numbers result for a bifurcating process with an infinite moving average representation

2012 ◽  
Vol 82 (1) ◽  
pp. 123-129 ◽  
Author(s):  
Jeff T. Terpstra ◽  
Tamer Elbayoumi
Keyword(s):  
Law Of Large Numbers ◽  
Moving Average ◽  
Large Numbers ◽  
Moving Average Representation ◽  
Average Representation

scholarly journals Limit theorems for locally stationary processes

2020 ◽  
Author(s):  
Rafael Kawka
Keyword(s):  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Moving Average ◽  
Stationary Processes ◽  
Time Varying ◽  
Strong Law ◽  
Large Numbers ◽  
Moving Average Representation ◽  
Locally Stationary Processes ◽  
Average Representation

Abstract We present limit theorems for locally stationary processes that have a one sided time-varying moving average representation. In particular, we prove a central limit theorem (CLT), a weak and a strong law of large numbers (WLLN, SLLN) and a law of the iterated logarithm (LIL) under mild assumptions using a time-varying Beveridge–Nelson decomposition.

Hilbert Spaces Formed by Strongly Harmonizable Stable Processes

2001 ◽  
Vol 8 (1) ◽  
pp. 181-188
Author(s):  
A. R. Soltani ◽  
B. Tarami
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Continuous Time ◽  
Moving Average ◽  
Stable Process ◽  
Stable Processes ◽  
Moving Average Representation ◽  
Process Elements ◽  
Average Representation

Abstract A strongly harmonizable continuous time symmetric α-stable process is considered. By using covariations, a Hilbert space is formed from the process elements and used for a purpose of moving average representation and prediction.

Solutions of Linear Rational Expectations Models

1985 ◽  
Vol 1 (3) ◽  
pp. 341-368 ◽  
Author(s):  
L. Broze ◽  
C. Gourieroux ◽  
A. Szafarz
Keyword(s):  
Rational Expectations ◽  
Moving Average ◽  
Stationary Solutions ◽  
Global Approach ◽  
Number Of Solutions ◽  
Simultaneous Treatment ◽  
Moving Average Representation ◽  
Natural Parametrization ◽  
Average Representation ◽  
Independent Parameters

Linear rational expectations models generally have a large number of solutions. It is thus important to describe them exhaustively in order to study their properties and subsequently estimate which solution best fits the data. In this paper, a global approach is suggested allowing a simultaneous treatment of all possible cases. The fundamental concepts are the revision processes appearing in the procedure of updating expectations. It isfound that the set of solutions is completely described by using a limitednumber of these processes. We show how the method may be applied to determine the set of stationary solutions admitting an infinite moving-average representation. We give a natural parametrization of this set and discuss the exact number of independent parameters.

A REMARK ON THE STRONG LAW FOR B-VALUED ARRAYS OF RANDOM ELEMENTS

2010 ◽  
Vol 82 (1) ◽  
pp. 31-43 ◽  
Author(s):  
TIEN-CHUNG HU ◽  
PING YAN CHEN ◽  
N. C. WEBER
Keyword(s):  
Law Of Large Numbers ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Strong Law ◽  
Rate Law ◽  
Large Numbers ◽  
Random Elements

AbstractThe conditions in the strong law of large numbers given by Li et al. [‘A strong law for B-valued arrays’, Proc. Amer. Math. Soc.123 (1995), 3205–3212] for B-valued arrays are relaxed. Further, the compact logarithm rate law and the bounded logarithm rate law are discussed for the moving average process based on an array of random elements.

On the asymptotic distributions of maxima of trigonometric polynomials with random coefficients

1984 ◽  
Vol 16 (4) ◽  
pp. 819-842 ◽  
Author(s):  
K. F. Turkman ◽  
A. M. Walker
Keyword(s):  
Moving Average ◽  
Random Coefficients ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Trigonometric Polynomials ◽  
Stationary Gaussian Sequence ◽  
Moving Average Representation ◽  
Standard Normal ◽  
Average Representation ◽  
Mutually Independent

Let {ε t, t = 1, 2, ···, n} be a sequence of mutually independent standard normal random variables. Let Xn(λ) and Yn(λ) be respectively the real and imaginary parts of exp iλ t, and let . It is shown that as n tends to∞, the distribution functions of the normalized maxima of the processes {Xn(λ)}, (Yn(λ)}, {In(λ)} over the interval λ∈ [0,π] each converge to the extremal distribution function exp [–e–x], —∞ < x <∞.It is also shown that these results can be extended to the case where {ε t} is a stationary Gaussian sequence with a moving-average representation.

A REPRESENTATION THEORY FOR POLYNOMIAL COFRACTIONALITY IN VECTOR AUTOREGRESSIVE MODELS

2009 ◽  
Vol 26 (4) ◽  
pp. 1201-1217 ◽  
Author(s):  
Massimo Franchi
Keyword(s):  
Representation Theory ◽  
Autoregressive Model ◽  
Moving Average ◽  
Recursive Algorithm ◽  
Autoregressive Models ◽  
Vector Autoregressive Models ◽  
Vector Autoregressive ◽  
Moving Average Representation ◽  
Average Representation

We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008, Econometric Theory 24, 651–676). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given, and it is shown under which condition the solution of the model is fractional of order d and displays cofractional relations of order d − b and polynomial cofractional relations of order d − 2b,…, d − cb ≥ 0 for integer c; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For c = 1 and c = 2 we find the results of Johansen (2008).

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