H. Peter Boswijk, Giuseppe Cavaliere, Anders Rahbek, Iliyan Georgiev
arXiv 10 Jan 2021 · Econometrics · publishedJournal of Econometrics (2019) · 1 citations (OpenAlex)
arXiv:2101.03562 · PDF · DOI · OpenAlex · Extracted main text
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated volatility processes as well as near-integrated GARCH processes. This paper develops conditions for bootstrap validity in time series regressions with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proving bootstrap validity, involving weak convergence in probability of the bootstrap statistic, fail to deliver the required results. Instead, we use the concept of `weak convergence in distribution' to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change and testing for an autoregressive unit root. Sufficient conditions for bootstrap validity include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results are illustrated using Monte Carlo simulations, which indicate that the wild bootstrap leads to size control even in small samples.
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 | Cavaliere, G.\ and I.\ Georgiev (2020) Inference Under Random Limit Bootstrap Measures self | 1.000 | 14 | 5 | 100% |
| 2 | Basawa, I., A.\ Mallik, W.\ McCormick, J.\ Reeves and R.\ Taylor (1991) Bootstrapping Unstable First-Order Autoregressive Processes ,\ | 0.843 | 3 | 3 | 100% |
| 3 | Hansen, B.\ E.\ (1995) Regression with Nonstationary Volatility ,\ | 0.811 | 4 | 2 | 100% |
| 4 | Cavaliere, G.\ and A.\ M.\ R.\ Taylor (2009) Heteroskedastic Time Series with a Unit Root ,\ self | 0.737 | 3 | 2 | 100% |
| 5 | Boswijk, H.\ P., G.\ Cavaliere, A.\ Rahbek and A.\ M.\ R.\ Taylor (2016) Inference on Co-Integration Parameters in Heteroskedastic Vector Autoregressions ,\ self | 0.644 | 2 | 2 | 100% |
| 6 | Nelson, D.\ B.\ (1990) ARCH Models as Diffusion Approximations ,\ | 0.644 | 2 | 2 | 100% |
| 7 | Cavaliere, G., H.\ B.\ Nielsen and A.\ Rahbek (2015) Bootstrap Testing of Hypotheses on Cointegration Relations in VAR Models ,\ self | 0.511 | 2 | 1 | 100% |
| 8 | Cavaliere, G., A.\ Rahbek and A.\ M.\ R.\ Taylor (2010) Testing for Co-Integration in Vector Autoregressions with Non-Stationary Volatility ,\ self | 0.511 | 2 | 1 | 100% |
| 9 | Cavaliere, G.\ and A.\ M.\ R.\ Taylor (2008) Bootstrap Unit Root Tests for Time Series with Nonstationary Volatility ,\ self | 0.511 | 2 | 1 | 100% |
| 10 | Goggin, E.\ M.\ (1994) Convergence in Distribution of Conditional Expectations ,\ | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 38 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 for an Explosive Bubble using High-Frequency Volatility | 0.405 | 1 | 1 |