Moving Average Representation and Prediction for Multidimensional Harmonizable Processes

2004 ◽  
Author(s):  
Marc Mehlman
Keyword(s):  
Moving Average ◽  
Moving Average Representation ◽  
Harmonizable Processes ◽  
Average Representation

scholarly journals A characterization and moving average representation for stable harmonizable processes

1996 ◽  
Vol 9 (3) ◽  
pp. 263-270 ◽  
Author(s):  
M. Nikfar ◽  
A. Reza Soltani
Keyword(s):  
Banach Space ◽  
Moving Average ◽  
Random Measure ◽  
Parameter Spaces ◽  
Borel Field ◽  
Moving Average Representation ◽  
Harmonizable Processes ◽  
Stable Random Variables ◽  
Set Function ◽  
Average Representation

In this paper we provide a characterization for symmetric α-stable harmonizable processes for 1<α≤2. We also deal with the problem of obtaining a moving average representation for stable harmonizable processes discussed by Cambanis and Soltani [3], Makegan and Mandrekar [9], and Cambanis and Houdre [2]. More precisely, we prove that if Z is an independently scattered countable additive set function on the Borel field with values in a Banach space of jointly symmetric α-stable random variables, 1<α≤2, then there is a function k∈L2(λ) (λ is the Lebesgue measure) and a certain symmetric-α-stable random measure Y for which ∫−∞∞eitxdZ(x)=∫−∞∞k(t−s)dY(s),t∈R, if and only if Z(A)=0 whenever λ(A)=0. Our method is to view SαS processes with parameter space R as SαS processes whose parameter spaces are certain Lβ spaces.

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.

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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