Counting Process Generated by Boundary-crossing Events. Theory and Statistical Applications
In this paper, we introduce and analyze a new class of stochastic process, named Boundary Crossing Counting Process. We show how to assess its finite-sample probability distribution using first exit time distributions. We discuss and calibrate three different methods for estimating this probability distribution and show how to use this distribution for non-parametric statistical specification testing or model validation. We apply this tool to the problem of unit root testing and to the problem of modeling financial data. First, we find that the BCC-test is less powerful than specific parametric unit-root tests, yet more powerful than another non-parametric test based on probability integral transform. Next, we learn that the BCC-test is relatively powerful in differentiating between commonly used GARCH type of models when the model under the null hypothesis and the model under the alternative hypothesis differ in the distribution of the error term. Finally, we show that the BCC-test often rejects the null hypothesis that the data generating process for major American and Australian stock indexes is well represented by the GARCH(1,1) model. The BCC-test cannot reject the GJR model for any specification, which is additional supportive evidence for the presence and importance of asymmetry in financial markets.
|Date of creation:||16 May 2013|
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- Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
- Andrew W. Lo, A. Craig MacKinlay, 1988.
"Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test,"
Review of Financial Studies,
Society for Financial Studies, vol. 1(1), pages 41-66.
- Tom Doan, . "VRATIO: RATS procedure to implement variance ratio unit root test procedure," Statistical Software Components RTS00231, Boston College Department of Economics.
- Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991.
"Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?,"
Cowles Foundation Discussion Papers
979, Cowles Foundation for Research in Economics, Yale University.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Tom Doan, . "KPSS: RATS procedure to perform KPSS (Kwiatowski, Phillips, Schmidt, and Shin) stationarity test," Statistical Software Components RTS00100, Boston College Department of Economics.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
- Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-87.
- Ait-Sahalia, Yacine, 1996.
"Testing Continuous-Time Models of the Spot Interest Rate,"
Review of Financial Studies,
Society for Financial Studies, vol. 9(2), pages 385-426.
- Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Caner, Mehmet & Kilian, Lutz, 2000.
"Size Distortions Of Tests Of The Null Hypothesis Of Stationarity: Evidence And Implications For The PPP Debate,"
CEPR Discussion Papers
2425, C.E.P.R. Discussion Papers.
- Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
- Kilian, L. & Caner, M., 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate," Papers 99-05, Michigan - Center for Research on Economic & Social Theory.
- Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- Hong, Yongmiao & Lee, Yoon-Jin, 2007. "An Improved Generalized Spectral Test For Conditional Mean Models In Time Series With Conditional Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(01), pages 106-154, February.
- Sheldon Lin, X., 1998. "Double barrier hitting time distributions with applications to exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 45-58, October.
- Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(05), pages 844-882, October.
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