Niklas Ahlgren, Alexander Back, Timo Teräsvirta
arXiv 4 Oct 2024 · Econometrics
arXiv:2410.03239 · PDF · DOI · OpenAlex · Extracted main text
It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a standard GARCH model by a deterministic time-varying intercept. It captures structural change that slowly affects the amplitude of a time series while keeping the short-run dynamics constant. We parameterize the intercept as a linear combination of logistic transition functions. We show that the model can be derived from a multiplicative decomposition of volatility and preserves the financial motivation of variance decomposition. We use the theory of locally stationary processes to show that the quasi maximum likelihood estimator (QMLE) of the parameters of the model is consistent and asymptotically normally distributed. We examine the quality of the asymptotic approximation in a small simulation study. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model. We find that the persistence implied by the GARCH parameter estimates is reduced by including a time-varying intercept in the volatility equation.
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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 | Subba Rao, Suhasini (2006) On Some Nonstationary, Nonlinear Random Processes and Their Stationary Approximations | 0.941 | 6 | 3 | 83% |
| 2 | Amado, Cristina, Teräsvirta, Timo (2013) Modelling volatility by variance decomposition self | 0.874 | 5 | 2 | 100% |
| 3 | Dahlhaus, Rainer (2006) Statistical Inference for Time-Varying ARCH Processes | 0.843 | 4 | 3 | 75% |
| 4 | Francq, Christian, Zakoïan, Jean-Michel (2004) Maximum Likelihood Estimation of Pure GARCH and ARMA-GARCH Processes | 0.763 | 9 | 4 | 44% |
| 5 | Chen, Bin, Hong, Yongmiao (2016) Detecting for smooth structural changes in GARCH models | 0.737 | 3 | 2 | 100% |
| 6 | Engle, Robert F, Siriwardane, Emil N (2018) Structural GARCH: the volatility-leverage connection | 0.644 | 2 | 2 | 100% |
| 7 | McAleer, Michael, Ling, Shiqing (2002) Necessary and sufficient moment conditions for the GARCH(r, s) and asymmetric power GARCH(r, s) models | 0.644 | 2 | 2 | 100% |
| 8 | Taylor, Stephen J (1986) Modelling Financial Time Series | 0.644 | 2 | 2 | 100% |
| 9 | Truquet, Lionel (2017) Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models | 0.644 | 2 | 2 | 100% |
| 10 | Dahlhaus, Rainer (1997) Fitting time series models to nonstationary processes | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 66 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Testing parametric additive time-varying GARCH models | 0.405 | 1 | 1 |