scholarly journals On the Unique Representation of Non-Gaussian Linear Processes

1992 ◽  
Vol 20 (2) ◽  
pp. 1143-1145 ◽  
Author(s):  
Qiansheng Cheng
Keyword(s):  
Linear Processes ◽  
Unique Representation ◽  
Non Gaussian

The distributional structure of finite moving-average processes

1988 ◽  
Vol 25 (02) ◽  
pp. 313-321 ◽  
Author(s):  
ED McKenzie
Keyword(s):  
Moving Average ◽  
Markov Property ◽  
Covariance Structure ◽  
Time Reversibility ◽  
Linear Processes ◽  
Joint Distributions ◽  
Moving Average Processes ◽  
Standard Models ◽  
Non Gaussian ◽  
Analysis Of Time Series

Analysis of time-series models has, in the past, concentrated mainly on second-order properties, i.e. the covariance structure. Recent interest in non-Gaussian and non-linear processes has necessitated exploration of more general properties, even for standard models. We demonstrate that the powerful Markov property which greatly simplifies the distributional structure of finite autoregressions has an analogue in the (non-Markovian) finite moving-average processes. In fact, all the joint distributions of samples of a qth-order moving average may be constructed from only the (q + 1)th-order distribution. The usefulness of this result is illustrated by references to three areas of application: time-reversibility; asymptotic behaviour; and sums and associated point and count processes. Generalizations of the result are also considered.

scholarly journals Deconvolution of non-Gaussian linear processes with vanishing spectral values

2011 ◽  
pp. 375-376
Author(s):  
Richard A. Davis ◽  
Keh-Shin Lii ◽  
Dimitris N. Politis
Keyword(s):  
Linear Processes ◽  
Non Gaussian

Linear processes and bispectra

1980 ◽  
Vol 17 (01) ◽  
pp. 265-270 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Frequency Response Function ◽  
Moving Average ◽  
Random Variables ◽  
Linear Process ◽  
Linear Filter ◽  
Linear Phase ◽  
Linear Processes ◽  
Spectral Estimates ◽  
Non Gaussian ◽  
Independent Identically Distributed

A linear process is generated by applying a linear filter to independent, identically distributed random variables. Only the modulus of the frequency response function can be estimated if only the linear process is observed and if the independent identically distributed random variables are Gaussian. In this case a number of distinct but related problems coalesce and the usual discussion of these problems assumes, for example, in the case of a moving average that the zeros of the polynomial given by the filter have modulus greater than one. However, if the independent identically distributed random variables are non-Gaussian, these problems become distinct and one can estimate the transfer function under appropriate conditions except for a possible linear phase shift by using higher-order spectral estimates.

Cumulant-based autocorrelation estimates of non-Gaussian linear processes

1995 ◽  
Vol 47 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Georgios B. Giannakis ◽  
Anastasios Delopoulos
Keyword(s):  
Linear Processes ◽  
Non Gaussian

The distributional structure of finite moving-average processes

1988 ◽  
Vol 25 (2) ◽  
pp. 313-321 ◽  
Author(s):  
ED McKenzie
Keyword(s):  
Moving Average ◽  
Markov Property ◽  
Covariance Structure ◽  
Time Reversibility ◽  
Linear Processes ◽  
Joint Distributions ◽  
Moving Average Processes ◽  
Standard Models ◽  
Non Gaussian ◽  
Analysis Of Time Series

Analysis of time-series models has, in the past, concentrated mainly on second-order properties, i.e. the covariance structure. Recent interest in non-Gaussian and non-linear processes has necessitated exploration of more general properties, even for standard models. We demonstrate that the powerful Markov property which greatly simplifies the distributional structure of finite autoregressions has an analogue in the (non-Markovian) finite moving-average processes. In fact, all the joint distributions of samples of a qth-order moving average may be constructed from only the (q + 1)th-order distribution. The usefulness of this result is illustrated by references to three areas of application: time-reversibility; asymptotic behaviour; and sums and associated point and count processes. Generalizations of the result are also considered.

Bispectra and phase of non-Gaussian linear processes

1993 ◽  
Vol 6 (3) ◽  
pp. 579-593 ◽  
Author(s):  
Keh-Shin Lii ◽  
Murray Rosenblatt
Keyword(s):  
Linear Processes ◽  
Non Gaussian
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