arXiv 15 Apr 2019 · Econometrics
arXiv:1904.07089 · PDF · DOI · OpenAlex · Extracted main text
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications we also obtain stationarity and $\beta$-mixing with subgeometrically decaying mixing coefficients.
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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) Subgeometric ergodicity and $$-mixing self | 1.000 | 7 | 4 | 100% |
| 2 | Fort, G. and E. Moulines (2003) Polynomial ergodicity of Markov transition kernels | 0.897 | 18 | 6 | 72% |
| 3 | Meyn, S. P. and R. L. Tweedie (2009) Markov Chains and Stochastic Stability\/ (2nd ed.) | 0.874 | 9 | 4 | 67% |
| 4 | Tuominen, P. and R. L. Tweedie (1994) Subgeometric rates of convergence of $f$-ergodic Markov chains | 0.843 | 3 | 3 | 100% |
| 5 | Douc, R., G. Fort, E. Moulines, and P. Soulier (2004) Practical drift conditions for subgeometric rates of convergence | 0.837 | 29 | 6 | 59% |
| 6 | Klokov, S. A (2007) Lower bounds of mixing rate for a class of Markov processes | 0.811 | 4 | 2 | 100% |
| 7 | Lu, Z (1998) On the geometric ergodicity of a non-linear autoregressive model with an autoregressive conditional heteroscedastic term | 0.737 | 3 | 3 | 67% |
| 8 | Douc, R., E. Moulines, P. Priouret, and P. Soulier (2018) Markov Chains | 0.737 | 3 | 2 | 100% |
| 9 | Klokov, S. A. and A. Y. Veretennikov (2004) Sub-exponential mixing rate for a class of Markov chains | 0.737 | 3 | 2 | 100% |
| 10 | Bec, F., A. Rahbek, and N. Shephard (2008) The ACR model: a multivariate dynamic mixture autoregression | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 28 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Subgeometric ergodicity and $$-mixing | 0.950 | 7 | 3 |
| 2 | Subgeometrically ergodic autoregressions with autoregressive conditional heteroskedasticity | 0.916 | 26 | 5 |