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How to test whether sign of coefficient of an independent variable depends on the direction of change in the independent variable itself?
How to test whether sign of coefficient of an independent variable depends on the direction of change in the independent variable itself?

I have 2 time series variables, x and y, the relationship between which I want to describe as y=a+bx where ‘a’ and ‘b’ are the parameters. The hypothesis is that the sign of ‘b’ is itself dependent on the direction of change in ‘x’, such that b<0 when dx/dt >0 and b>0 when dx/dt<0. Could you please suggest what would be the best way to test this hypothesis?

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