arXiv 24 May 2022 · Econometrics · publishedEconometric Theory (2023) · 1 citations (OpenAlex)
arXiv:2205.11953 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in 1980s and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $\beta$-mixing coefficients. While the existing literature on subgeometrically ergodic autoregressions assumes a homoskedastic error term, this paper provides an extension to the case of conditionally heteroskedastic ARCH-type errors, considerably widening the scope of potential applications. Specifically, we consider suitably defined higher-order nonlinear autoregressions with possibly nonlinear ARCH errors and show that they are, under appropriate conditions, subgeometrically ergodic at a polynomial rate. An empirical example using energy sector volatility index data illustrates the use of subgeometrically ergodic AR-ARCH models.
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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 | Fort, G. and E. Moulines (2003) Polynomial ergodicity of Markov transition kernels | 1.000 | 8 | 4 | 100% |
| 2 | Douc, R., G. Fort, E. Moulines, and P. Soulier (2004) Practical drift conditions for subgeometric rates of convergence | 1.000 | 6 | 3 | 100% |
| 3 | Meitz, M. and P. Saikkonen (2022) Subgeometrically ergodic autoregressions self | 0.916 | 26 | 5 | 77% |
| 4 | Meitz, M. and P. Saikkonen (2010) A note on the geometric ergodicity of a nonlinear AR–ARCH model self | 0.843 | 4 | 4 | 75% |
| 5 | Cline, D. B. H. and H. H. Pu (2004) Stability and the Lyapounov exponent of threshold AR–ARCH models | 0.843 | 3 | 3 | 100% |
| 6 | Meitz, M. and P. Saikkonen (2008) Stability of nonlinear AR–GARCH models self | 0.811 | 4 | 2 | 100% |
| 7 | Horn, R. A. and C. R. Johnson (2013) Matrix Analysis\/ (2nd ed.) | 0.763 | 9 | 2 | 67% |
| 8 | Meyn, S. P. and R. L. Tweedie (2009) Markov Chains and Stochastic Stability\/ (2nd ed.) | 0.754 | 7 | 3 | 43% |
| 9 | Fefferman, C. and H. S. Shapiro (1972) A planar face on the unit sphere of the multiplier space $M_p$, $1<p<$ | 0.737 | 3 | 3 | 67% |
| 10 | Douc, R., E. Moulines, P. Priouret, and P. Soulier (2018) Markov Chains | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 37 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Robust Estimation in Network Vector Autoregression with Nonstationary Regressors | 0.644 | 2 | 2 |
| 2 | Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models | 0.405 | 1 | 1 |