The Variance Ratio Statistic at large Horizons
We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k/n ¨0. The test is shown to be consistent against a variety of relevant mean reverting alternatives when k/n ¨0. This is in contrast to the case when k/n ¨ƒÂ>0, where the statistic has been recently shown to be inconsistent against such alternatives. Secondly, we provide and justify a simple power transformation of the statistic which yields almost perfectly normally distributed statistics in finite samples, solving the well known right skewness problem. Thirdly, we provide a more powerful way of pooling information from different horizons to test for mean reverting alternatives. Monte Carlo simulations illustrate the theoretical improvements provided.
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- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Andrew W. Lo & A. Craig MacKinlay, 1988.
"The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation,"
NBER Technical Working Papers
0066, National Bureau of Economic Research, Inc.
- Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February.
- Andrew W. Lo & Craig A. MacKinlay, . "The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation," Rodney L. White Center for Financial Research Working Papers 28-87, Wharton School Rodney L. White Center for Financial Research.
- Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
- Poterba, James M. & Summers, Lawrence H., 1988.
"Mean reversion in stock prices : Evidence and Implications,"
Journal of Financial Economics,
Elsevier, vol. 22(1), pages 27-59, October.
- James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
- Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
- Campbell, John & Mankiw, Gregory, 1987.
"Are Output Fluctuations Transitory?,"
3122545, Harvard University Department of Economics.
- 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.
- 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.
- Tom Doan, . "VRATIO: RATS procedure to implement variance ratio unit root test procedure," Statistical Software Components RTS00231, Boston College Department of Economics.
- Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
- Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Deo, Rohit S. & Richardson, Matthew, 2003. "On The Asymptotic Power Of The Variance Ratio Test," Econometric Theory, Cambridge University Press, vol. 19(02), pages 231-239, April.
- Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
- Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-26, September.
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