OLS between two stochastic variables

by user198021   Last Updated April 16, 2018 07:19 AM

I am confusing what we actually do when conducting OLS for the stochastic dependent time series and independent time series. Do we rearrange (y, x) pairs, for example, in terms of the size of Xt from the smallest value to the largest value, regardless of their temporal order? Then, we estimate how much the dv tends to change as Xt increase by one unit? In this case, I understand that we can discuss a linear relationship (OLS coefficient) between Yt and Xt. If we do not rearrange the (Y, X) pairs, then how can we discuss the linear relationship between Y and X, both of which stochastically fluctuate? Do we assume a kind of long-run increasing or decreasing tendency, which we usuaully term a trend, at least in Xt? Then OLS analysis is appropriate only for variables with a deterministic trend?

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