The model does not include an intercept and uses a dummy variable for each quartile of the AOII index to control for differences in daily average returns that may lead to spurious autocorrelations (Higgins, Howton and Perfect (2000)).
To test this relationship, Equation 2 will be estimated by regressing daily QQQ returns on the AOII dummy variables and the lagged market returns:
All of the returns are positive and statistically different from zero on days when the AOII fell in the first quartile.
The practical conclusion to this result is that investors should evaluate the AOII, if the index increases (decreases), implement the contrarion decision is to sell (buy).
The decision rule incorporates the interaction between a negative return on the Cube and the AOII ending between 12% to 40%, if these conditions are met, the investor should short-sell the Nasdaq 100 fund.