Mixing properties of ARMA processes

By Abdelkader Mokkadem. 1988

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Citations in the corpus

The Arrow of Time in Multivariate Time Series (2016, background): “demic but has received a lot of attention in literature, especially in physics, see Reichenbach (1956) or Price (1996).”
From Predictive to Prescriptive Analytics (2014, background): “hed that 2(k) (k) and 4(k) ˆ(k) so that either - or ˆ-mixing implies -mixing. Many processes satisfy mixing conditions under mild assumptions: auto-egressive moving-average (ARMA) processes (see [31]), generalized autoregressive conditional heteroskedasticity (GARCH) processes (see [12]), and certai”
Random Forests for dependent data (2020, methodology): “As ARMA processes are β-mixing [49], the process (`i) sampled on the integer lattice is proved to be β-mixing.”
Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes (2012, background): “[1, 19, 20]), the mixing properties of the innovations of a sampled continuoustime process have received very little attention in the past.”
A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing (2013, unknown): “The conditions of the above corollary are, for instance, satisfied (with much to spare) when X1, . . . ,Xn is drawn from a stationary vector ARMA process with absolutely continuous innovations (see Mokkadem [32]).”
Breaking the curse of dimensionality in regression (2017, unknown): “Many popular time series models including ARMA and GARCH satisfy this condition; see (Mokkadem, 1988; Carrasco and Chen, 2002).”
Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes (2005, background): “Suppose that et has a density which is positive on R. Applying Theorem 2 to the Markovian representation of the process, one obtains that fXtg is absolutely regular with mixing coefficients bk ¼ O(ck), c 2 (0, 1), cf. Mokkadem (1988).”