arXiv 4 Jun 2018 · Mathematics — Statistics Theory · publishedStatistics & Probability Letters (2019)
arXiv:1806.01229 · PDF · DOI · OpenAlex · Extracted main text
This paper develops the limit theory of the GARCH(1,1) process that moderately deviates from IGARCH process towards both stationary and explosive regimes. The GARCH(1,1) process is defined by equations $u_t = \sigma_t \varepsilon_t$, $\sigma_t^2 = \omega + \alpha_n u_{t-1}^2 + \beta_n\sigma_{t-1}^2$ and $\alpha_n + \beta_n$ approaches to unity as sample size goes to infinity. The asymptotic theory developed in this paper extends Berkes et al. (2005) by allowing the parameters to have a slower convergence rate. The results can be applied to unit root test for processes with mildly-integrated GARCH innovations (e.g. Boswijk (2001), Cavaliere and Taylor (2007, 2009)) and deriving limit theory of estimators for models involving mildly-integrated GARCH processes (e.g. Jensen and Rahbek (2004), Francq and Zako\"ian (2012, 2013)).
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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 | Berkes, I., Horváth, L., & Kokoszka, P (2005) Near-integrated garch sequences | 1.000 | 11 | 4 | 100% |
| 2 | Billingsley, P (1995) Probability and measure | 0.511 | 2 | 1 | 100% |
| * | unmatched citation key * | 0.405 | 1 | 1 | 100% |
| 4 | Boswijk, H. P (2001) Testing for a unit root with near-integrated volatility | 0.405 | 1 | 1 | 100% |
| 5 | Cavaliere, G., & Taylor, A. M. R (2007) Testing for unit roots in time series models with non-stationary volatility | 0.405 | 1 | 1 | 100% |
| 6 | Cavaliere, G., & Taylor, A. M. R (2009) Heteroskedastic time series with a unit root | 0.405 | 1 | 1 | 100% |
| 7 | Chow, Y. S., & Teicher, H (2012) Probability Theory: Independence, Interchangeability, Martingales | 0.405 | 1 | 1 | 100% |
| 8 | Francq, C., & Zakoïan, J.-M (2012) Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity… | 0.405 | 1 | 1 | 100% |
| 9 | Francq, C., & Zakoïan, J.-M (2013) Inference in nonstationary asymmetric garch models | 0.405 | 1 | 1 | 100% |
| 10 | Jensen, S. T., & Rahbek, A (2004) Asymptotic inference for nonstationary garch | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 10 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.