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Variance ratio test for random walk
h = vratiotest(y)
h = vratiotest(y,'ParameterName',ParameterValue,...)
[h,pValue] = vratiotest(...)
[h,pValue,stat] = vratiotest(...)
[h,pValue,stat,cValue] = vratiotest(...)
[h,pValue,stat,cValue,ratio] = vratiotest(...)
h = vratiotest(y) assesses the null hypothesis of a random walk in a univariate time series y.
h = vratiotest(y,'ParameterName',ParameterValue,...) accepts optional inputs as one or more comma-separated parameter-value pairs. 'ParameterName' is the name of the parameter inside single quotation marks. ParameterValue is the value corresponding to 'ParameterName'. Specify parameter-value pairs in any order; names are case-insensitive. Perform multiple tests by passing a vector value for any parameter. Multiple tests yield vector results.
[h,pValue] = vratiotest(...) returns p-values of the test statistics.
[h,pValue,stat] = vratiotest(...) returns the test statistics.
[h,pValue,stat,cValue] = vratiotest(...) returns critical values for the tests.
[h,pValue,stat,cValue,ratio] = vratiotest(...) returns a vector of ratios.
The variance ratio test assesses the null hypothesis that a univariate time series y is a random walk. The null model is
y(t) = c + y(t–1) + e(t),
where c is a drift constant and e(t) are uncorrelated innovations with zero mean.
When IID is false, the alternative is that the e(t) are correlated.
When IID is true, the alternative is that the e(t) are either dependent or not identically distributed (for example, heteroscedastic).
[1] Campbell, J. Y., A. W. Lo, and A. C. MacKinlay. Chapter 12. "The Econometrics of Financial Markets." Nonlinearities in Financial Data. Princeton, NJ: Princeton University Press, 1997.
[2] Cecchetti, S. G., and P. S. Lam. "Variance-Ratio Tests: Small-Sample Properties with an Application to International Output Data." Journal of Business and Economic Statistics. Vol. 12, 1994, pp. 177–186.
[3] Cochrane, J. "How Big is the Random Walk in GNP?" Journal of Political Economy. Vol. 96, 1988, pp. 893–920.
[4] Faust, J. "When Are Variance Ratio Tests for Serial Dependence Optimal?" Econometrica. Vol. 60, 1992, pp. 1215–1226.
[5] Lo, A. W., and A. C. MacKinlay. "Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test." Review of Financial Studies. Vol. 1, 1988, pp. 41–66.
[6] Lo, A. W., and A. C. MacKinlay. "The Size and Power of the Variance Ratio Test." Journal of Econometrics. Vol. 40, 1989, pp. 203–238.
[7] Lo, A. W., and A. C. MacKinlay. A Non-Random Walk Down Wall St. Princeton, NJ: Princeton University Press, 2001.