I have a statistics question that eventually would be implemented in R but
my question is what to do statistically.

 

Suppose I have a model Y_t = Beta*X_t-1 and Y_t and X_t are both univariate.
Y_t can be negative or positive but generally ranges

Between -.0010 and + .0010.  I can estimate Beta using lm but that's not
really my goal. I know that X_t-1 is an okay predictor

of Y_t but what I really want to do is estimate the value of  X_t-1 such
that abs(Y_t) is greater than a constant say thresh which I can specify.

 

I was thinking of using some kind of Probit or Logit where I define the
event as Y_t* = 1 when abs(Y_t) > thresh and zero otherwise ?

 

Does anyone know if using Probit or Logit is a reasonable approach or should
I estimate the linear regression and then somehow infer the X_t-1

that satisfies the threshold relationship ? I'm not even clear if I should
be estimating a Beta ? Maybe I should be estimating the empirical CDF of Y_t

but the CDF is definitely dependent on  X_t-1.  Thanks for any suggestions,
references etc. It's not a homework problem :-)

 

 

 

 

 


	[[alternative HTML version deleted]]

