Simon Clinet, Yoann Potiron
arXiv 17 May 2019 · Finance — Statistical Finance · publishedElectronic Journal of Statistics (2021)
arXiv:1905.07081 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method and show the related consistency and central limit theory when there is cointegration within that framework. We also provide a Dickey-Fuller type residual based test for the null of no cointegration against the alternative of cointegration, along with its limit theory. Under no cointegration, the asymptotic limit is the same as that of the original Dickey-Fuller residual based test, so that critical values can be easily tabulated in the same way. Finite sample indicates adequate size and good power properties in a variety of realistic configurations, outperforming original Dickey-Fuller and Phillips-Perron type residual based tests, whose sizes are distorted by non ergodic time-varying variance and power is altered by price jumps. Two empirical examples consolidate the Monte-Carlo evidence that the adapted tests can be rejected while the original tests are not, and vice versa.
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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 | Beare, B. K (2018) Unit root testing with unstable volatility | 1.000 | 8 | 4 | 100% |
| 2 | Phillips, P. C. and Ouliaris, S (1990) Asymptotic properties of residual based tests for cointegration | 1.000 | 8 | 4 | 100% |
| 3 | Engle, R. F. and Granger, C. W (1987) Co-integration and error correction: representation, estimation, and testing | 1.000 | 7 | 3 | 100% |
| 4 | Gregory, A. W. and Hansen, B. E (1996) Residual-based tests for cointegration in models with regime shifts | 0.843 | 3 | 3 | 100% |
| 5 | Maki, D (2012) Tests for cointegration allowing for an unknown number of breaks | 0.843 | 3 | 3 | 100% |
| 6 | Mancini, C (2009) Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps | 0.843 | 3 | 3 | 100% |
| 7 | Phillips, P. C (1987) Time series regression with a unit root | 0.737 | 3 | 3 | 67% |
| 8 | Aẗ-Sahalia, Y. and Xiu, D (2019) A Hausman test for the presence of market microstructure noise in high frequency data | 0.737 | 3 | 2 | 100% |
| 9 | Kim, C. S. and Park, J. Y (2010) Cointegrating regressions with time heterogeneity | 0.737 | 3 | 2 | 100% |
| 10 | Cavaliere, G. and Taylor, A. R (2007) Testing for unit roots in time series models with non-stationary volatility | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 57 scored citations.