Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes

By Eckhard Liebscher. 2005

116 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c0b7412b58000192ef878b4f33a06c2bc5b60559

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Marc Hallin
2. Stanislav Volgushev
3. Holger Dette
4. Pentti Saikkonen
5. Piotr Fryzlewicz
6. S. Rao
7. Tobias Kley

Citations in the corpus

• Stability of nonlinear AR‐GARCH models (2008, unknown): “From Theorem 1 and Proposition 5 of Liebscher (2005) we can then conclude that a sufficient condition for Lemma 1(i), and hence, Assumption 3 is that the joint spectral radius of the set of two matrices {A1, A2} is smaller than one, or that ρ ({A1, A2}) 1.”
• Ergodicity and invertibility of threshold moving-average models (2007, unknown): “Further related results can be found in Chen and Tsay (1991), Brockwell et al. (1992), Liu and Susko (1992), An and Huang (1996), An and Chen (1997), Liu et al. (1997), Ling (1999), Cline and Pu (1999, 2004), Lanne and Saikkonen (2005), Liebscher (2005) and others.”
• Mixing properties of ARCH and time-varying ARCH processes (2011, background): “Related results on mixing for GARCH(p, q) processes can be found in [8, 25, 26, 35] (for an excellent review) and [14, 27] (where mixing of ‘nonlinear’ GARCH(p, q) processes is also considered).”
• STABILITY OF REGIME SWITCHING ERROR CORRECTION MODELS UNDER LINEAR COINTEGRATION (2007, methodology): “that the autoregressive coefficients in the highest and lowest regimes are smaller than one in absolute value (see Theorem 5 of Liebscher (2005) ).”
• Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis (2011, background): “The class of β-mixing processes is well studied, and contains a wide range of linear and nonlinear processes, including (possibly, under mild additional assumptions) ARMA, general nonlinear scalar ARCH, threshold ARCH, and exponential ARCH processes (see Liebscher [32]), GARCH(p, q) processes with m”
• PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS (2011, unknown): “Several useful results about the joint spectral radius are given in the recent paper by Liebscher (2005) where further references can also be found; see also Meitz and Saikkonen (2008c).”