Extending the variance ratio test to visualize structure in data: an application to the S&P 100 Index

The aim of this paper is to present a method able to graphically describe the amount of structure in a time series. In the following, 'structure' is defined as the extent to which a time series is either trending or mean-reverting (that is showing pockets of positive as well as negative autocorrelation). What is defined as being trending, respectively mean-reverting, should be seen in relation to the characteristics of a random walk. Testing most of the constituents of the Standard & Poor's 100 index for structure and using a modified variance ratio that focuses on the whole ratio profile rather than an individual ratio, trending is detected as well as mean-reverting structure over a time period of more than 10 years.