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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