When it comes to threshold linear regression, in order to estimate it can we simply divide our dataset according to the threshold rule into 2 datasets and then simply estimate 2 equations with OLS? Or am I missing something important?
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$\begingroup$ Do you know the changepoint or not? If you don't know it, how do you propose to partition the dataset? If you do know it, how will you assure your continuity or differentiability criteria will be met at the changepoint and how will you assure a homoscedastic response? $\endgroup$– whuber ♦Commented Oct 13, 2022 at 20:54
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$\begingroup$ For simplicity I assume the threshold to be known. I'm not sure I understand your second question, the regression function would be continuous since for one regime condition is "greater than" and the other "lesser or equal than". While dealing with possible threshold we are dealing with nonlinear regression - so threshold should decrease pot. heteroskedasticity as I see it $\endgroup$– FatafimCommented Oct 13, 2022 at 20:58
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$\begingroup$ The threshold and the heteroscedasticity are different issues. When you split the data into two parts you will inevitably obtain two different estimates of the error variance, making that an inherently heteroscedastic model. Research our threads on changepoint analyses. Furthermore, when you split the data you almost surely will obtain a discontinuous response function. $\endgroup$– whuber ♦Commented Oct 14, 2022 at 12:59
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$\begingroup$ If so, then I can still do inference treating them separately I suppose. The question is, whether this approach is correct, or TLM are estimated in a different way? The link you've attached is too general for me, I'm not sure what exactly you want me to research. $\endgroup$– FatafimCommented Oct 14, 2022 at 13:46
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