scholarly journals A closed-form identification of multichannel moving average processes by ESPRIT

1996 ◽  
Vol 15 (3) ◽  
pp. 343-359 ◽  
Author(s):  
Lang Tong ◽  
Rueywen Liu
Keyword(s):  
Closed Form ◽  
Moving Average ◽  
Form Identification ◽  
Moving Average Processes

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.

Fourth Moment Structure of Markov Switching Multivariate GARCH Models

2019 ◽  
Author(s):  
Maddalena Cavicchioli
Keyword(s):  
Closed Form ◽  
Moving Average ◽  
Markov Switching ◽  
Computational Cost ◽  
Sufficient Conditions ◽  
Impulse Response Function ◽  
Real Data ◽  
Multivariate Garch ◽  
Fourth Moment ◽  
Spectral Density Matrix

Abstract We derive sufficient conditions for the existence of second and fourth moments of Markov switching multivariate generalized autoregressive conditional heteroscedastic processes in the general vector specification. We provide matrix expressions in closed form for such moments, which are obtained by using a Markov switching vector autoregressive moving-average representation of the initial process. These expressions are shown to be readily programmable in addition of greatly reducing the computational cost. As theoretical applications of the results, we derive the spectral density matrix of the squares and cross products, propose a new definition of multivariate kurtosis measure to recognize heavy-tailed features in financial real data, and provide a matrix expression in closed form of the impulse-response function for the volatility. An empirical example illustrates the results.

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