Lajos Horvath, Lorenzo Trapani, Shixuan Wang
arXiv 27 Apr 2024 · Econometrics
arXiv:2404.17885 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we develop two families of sequential monitoring procedure to (timely) detect changes in a GARCH(1,1) model. Whilst our methodologies can be applied for the general analysis of changepoints in GARCH(1,1) sequences, they are in particular designed to detect changes from stationarity to explosivity or vice versa, thus allowing to check for volatility bubbles. Our statistics can be applied irrespective of whether the historical sample is stationary or not, and indeed without prior knowledge of the regime of the observations before and after the break. In particular, we construct our detectors as the CUSUM process of the quasi-Fisher scores of the log likelihood function. In order to ensure timely detection, we then construct our boundary function (exceeding which would indicate a break) by including a weighting sequence which is designed to shorten the detection delay in the presence of a changepoint. We consider two types of weights: a lighter set of weights, which ensures timely detection in the presence of changes occurring early, but not too early after the end of the historical sample; and a heavier set of weights, called Renyi weights which is designed to ensure timely detection in the presence of changepoints occurring very early in the monitoring horizon. In both cases, we derive the limiting distribution of the detection delays, indicating the expected delay for each set of weights. Our theoretical results are validated via a comprehensive set of simulations, and an empirical application to daily returns of individual stocks.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
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 | Jensen, S. T. and A. Rahbek (2004) Asymptotic inference for nonstationary GARCH | 1.000 | 7 | 4 | 100% |
| 2 | Francq, C. and J.-M. Zakoän (2012) Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity… | 1.000 | 6 | 4 | 100% |
| 3 | Ghezzi, F., E. Rossi, and L. Trapani (2024) Fast online changepoint detection | 1.000 | 5 | 3 | 100% |
| 4 | Horváth, L. and S. Wang (2024) Detecting changes in GARCH(1, 1) processes without assuming stationarity | 0.874 | 7 | 2 | 100% |
| 5 | Berkes, I., L. Horváth, and P. Kokoszka (2003) GARCH processes: structure and estimation | 0.874 | 6 | 2 | 100% |
| 6 | Francq, C. and J.-M. Zakoian (2019) GARCH models: structure, statistical inference and financial applications | 0.874 | 5 | 2 | 100% |
| 7 | Horváth, L., Z. Liu, G. Rice, and S. Wang (2020) Sequential monitoring for changes from stationarity to mild non-stationarity | 0.843 | 3 | 3 | 100% |
| 8 | Horváth, L., C. Miller, and G. Rice (2021) Detecting early or late changes in linear models with heteroscedastic errors | 0.843 | 3 | 3 | 100% |
| 9 | Csörgo, M. and L. Horváth (1997) Limit Theorems in Change-Point Analysis, Volume 18 | 0.644 | 4 | 1 | 100% |
| 10 | Hillebrand, E (2005) Neglecting parameter changes in GARCH models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.