Stefan Richter, Weining Wang, Wei Biao Wu
arXiv 9 Dec 2018 · Econometrics · 1 citations (OpenAlex)
arXiv:1812.03475 · PDF · DOI · OpenAlex · Extracted main text
We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an 'abnormal' period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, and then provide an algorithm to identify the period of change. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the QMLE in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian Process. In simulations we show that the test has good size and power for reasonably large time series lengths. We apply the test to Apple asset returns and Bitcoin returns.
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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 | Christian Francq and Jean-Michel Zakoän (2004) Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes | 0.874 | 11 | 2 | 100% |
| 2 | Christian Francq and Jean-Michel Zakoän (2012) Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity… | 0.737 | 3 | 2 | 100% |
| 3 | D. Zhang and W. B. Wu (2017) Gaussian Approximation for High Dimensional Time Series | 0.737 | 3 | 2 | 100% |
| 4 | Wei Biao Wu and Xiaofeng Shao (2004) Limit theorems for iterated random functions self | 0.644 | 2 | 2 | 100% |
| 5 | Wei Biao Wu and Zhou Zhou (2011) Gaussian approximations for non-stationary multiple time series self | 0.644 | 2 | 2 | 100% |
| 6 | Sren Tolver Jensen and Anders Rahbek (2004) Asymptotic normality of the qmle estimator of arch in the nonstationary case | 0.511 | 2 | 1 | 100% |
| 7 | Daniel B Nelson (1990) Stationarity and persistence in the GARCH (1, 1) model | 0.405 | 1 | 1 | 100% |
| 8 | Marc S.\ Paolella (2018) Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH | 0.405 | 1 | 1 | 100% |
| 9 | István Berkes, Lajos Horváth, and Piotr Kokoszka (2003) GARCH processes: structure and estimation | 0.405 | 1 | 1 | 100% |
| 10 | Nick Bloom (2007) Uncertainty and the dynamics of R&D | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.