Variance Ratio Testing for multidimensional random walk

I'm interested in detecting whether a set of points in 3D space follows a trajectory that can be explained by a random walk. I've come across the Variance Ratio test used to analyze 1D data (time-series) to determine if the data follows a random walk. Is there a strategy to extend the Variance Ratio test to analyze multi-dimensional data (2D, 3D, etc.)?

Answer 1

[Pankhuri Kasliwal]

Typically, variance ratio test is done for one dimensional data. To perform such a test for more variables or 2D/3D data, you can use “anova” also known as analysis of variance. You can read more about anova in the link below - https://www.technologynetworks.com/informatics/articles/one-way-vs-two-way-anova-definition-differences-assumptions-and-hypotheses-306553

Refer to the documentation of anova for more details on how you can perform the test –

1. https://www.mathworks.com/help/stats/anovan.html
2. https://www.mathworks.com/help/stats/anova2.html