arXiv 15 Apr 2019 · Econometrics · publishedJournal of Applied Probability (2021) · 3 citations (OpenAlex)
arXiv:1904.07103 · PDF · DOI · OpenAlex · Extracted main text
It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$-mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$-mixing with subgeometrically decaying mixing coefficients. Although this result is simple it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity can not be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$-mixing results for the self-exciting threshold autoregressive model.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Meitz, M. and P. Saikkonen (2019) Subgeometrically ergodic autoregressions self | 0.950 | 7 | 3 | 86% |
| 2 | Douc, R., G. Fort, E. Moulines, and P. Soulier (2004) Practical drift conditions for subgeometric rates of convergence | 0.937 | 17 | 4 | 82% |
| 3 | Fort, G. and E. Moulines (2003) Polynomial ergodicity of Markov transition kernels | 0.928 | 5 | 3 | 80% |
| 4 | Liebscher, E (2005) Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes | 0.928 | 4 | 3 | 100% |
| 5 | Meyn, S. P. and R. L. Tweedie (2009) Markov Chains and Stochastic Stability\/ (2nd ed.) | 0.916 | 13 | 7 | 77% |
| 6 | Nummelin, E. and P. Tuominen (1983) The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory | 0.843 | 4 | 3 | 75% |
| 7 | Bradley, R. C (2007) Introduction to Strong Mixing Conditions, Volume -3pts 1–3 | 0.843 | 3 | 3 | 100% |
| 8 | Doukhan, P (1994) Mixing: Properties and Examples | 0.843 | 3 | 3 | 100% |
| 9 | Tuominen, P. and R. L. Tweedie (1994) Subgeometric rates of convergence of $f$-ergodic Markov chains | 0.737 | 4 | 3 | 50% |
| 10 | Douc, R., E. Moulines, P. Priouret, and P. Soulier (2018) Markov Chains | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 26 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Subgeometrically ergodic autoregressions | 1.000 | 7 | 4 |
| 2 | Subgeometrically ergodic autoregressions with autoregressive conditional heteroskedasticity | 0.644 | 2 | 2 |
| 3 | Robust Estimation in Network Vector Autoregression with Nonstationary Regressors | 0.405 | 1 | 1 |