arXiv 23 Jul 2018 · Statistics — Methodology · 5 citations (OpenAlex)
arXiv:1807.08390 · PDF · DOI · OpenAlex · Extracted main text
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.
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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 | C. Francq and J. M. Zakoian (2011) GARCH Models: Structure, Statistical Inference and Financial Applications | 1.000 | 5 | 4 | 100% |
| 2 | B. Cs. Csáji, M. C. Campi, and E. Weyer (2015) Sign-Perturbed Sums: A new system identification approach for constructing exact non-asymptotic confidence regions in linear reg… | 1.000 | 5 | 3 | 100% |
| 3 | L. Ljung (1999) System Identification: Theory for the User | 1.000 | 5 | 3 | 100% |
| 4 | D. Straumann (2005) Estimation in Conditionally Heteroscedastic Time Series Models | 0.928 | 4 | 3 | 100% |
| 5 | B. Cs. Csáji, M.C. Campi, and E. Weyer (2012) Sign-Perturbed Sums (SPS): A method for constructing exact finite-sample confidence regions for general linear systems | 0.874 | 5 | 2 | 100% |
| 6 | I. Berkes, L. Horváth, and P. Kokoszka (2003) GARCH processes: structure and estimation | 0.843 | 3 | 3 | 100% |
| 7 | B. Cs. Csáji, M. C. Campi, and E. Weyer (2014) Strong consistency of the Sign-Perturbed Sums method | 0.737 | 3 | 2 | 100% |
| 8 | T. Bollerslev (1986) Generalized autoregressive conditional heteroskedasticity | 0.644 | 2 | 2 | 100% |
| 9 | P. Good (2005) Permutation, Parametric, and Bootstrap Tests of Hypotheses | 0.644 | 2 | 2 | 100% |
| 10 | P. R. Hansen and A. Lunde (2005) A forecast comparison of volatility models: does anything beat a GARCH(1,1)? | 0.644 | 2 | 2 | 100% |
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