The Stochastic Recurrence Structure of Geophysical Phenomena

2015 ◽  
pp. 55-88 ◽  
Author(s):  
I. Javors’kyj ◽  
R. Yuzefovych ◽  
I. Matsko ◽  
I. Kravets
Keyword(s):  
Stochastic Recurrence

scholarly journals Analysis of rotary mechanism fault features on the base of the spectral structure for vibration stochastic recurrence

2019 ◽  
Vol 16 ◽  
pp. 205-210 ◽  
Author(s):  
Ihor Javorskyj ◽  
Roman Yuzefovych ◽  
Pavlo Semenov ◽  
Pavlo Kurapov
Keyword(s):  
Spectral Structure ◽  
Stochastic Recurrence ◽  
Fault Features ◽  
Rotary Mechanism

scholarly journals CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

2021 ◽  
pp. 1-34
Author(s):  
Muneya Matsui ◽  
Rasmus Søndergaard Pedersen
Keyword(s):  
Stationary Solutions ◽  
Tail Index ◽  
Recurrence Equation ◽  
Multivariate Garch ◽  
Tail Behavior ◽  
Stochastic Recurrence ◽  
Garch Processes ◽  
Strict Stationarity ◽  
Daily Returns

Abstract We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

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