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 :-)
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