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

[Zico Dasgupta]

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?

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.
First, with time series data, you need to tsset or xtset the data. The using lag pr difference operators (L. or D.) you can determine the change in x from one period to the next. Generate a dummy for positive change g poschg=(dxdt>0). Interact the dummy with x.

[Zico Dasgupta]

Thanks a lot Phil for your reply, this would be very helpful.