# vratiotest

Variance ratio test for random walk

## Syntax

## Description

returns
the rejection decision `h`

= vratiotest(`y`

)`h`

from conducting the variance ratio test for assessing
whether the univariate time series `y`

is a random walk.

returns the table `StatTbl`

= vratiotest(`Tbl`

)`StatTbl`

containing variables for the test results,
statistics, and settings from conducting the variance ratio test on the last variable of the
input table or timetable `Tbl`

. To select a different variable in
`Tbl`

to test, use the `DataVariable`

name-value
argument.

`[___] = vratiotest(___,`

specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
`Name=Value`

)`vratiotest`

returns the output argument combination for the
corresponding input arguments.

Some options control the number of tests to conduct. The following conditions apply when
`vratiotest`

conducts multiple tests:

For example,
`vratiotest(Tbl,DataVariable="GDP",Alpha=0.025,IID=[false true])`

conducts two tests, at a level of significance of 0.025, on the variable
`GDP`

of the table `Tbl`

. The first test does not assume
that the innovations series is iid and the second test assumes that the innovations series
is iid.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

The test finds the largest integer

*n*such that*n**q*≤*T*– 1, where*q*is the vaule of the`Period`

argument and*T*is the sample size. Then, the test discards the final (*T*–1) –*n**q*observations. To include these final observations, remove the initial (*T*–1) –*n**q*observations from the input series before you run the test.

## References

[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.

## Version History

**Introduced in R2009b**