I was wondering if we need the response variable to be ergodic stationarity when estimating an OLS spline regression. My intuition tells me that it's not needed but I would like to have a confirmation regarding it. Thanks in advance.

  • $\begingroup$ I've never heard of ergodicity being a necessary condition for the fulfilment of any property of OLS estimators. What motivated this question of yours? $\endgroup$ – Lucas Farias Feb 8 at 2:38
  • $\begingroup$ For example in time series analysis when dealing with big set of data, the ergodicity is a sort of weak "independence" between observations. In ols we need the observations to be i.i.d. but since in time series that is just imposible because of the "memory " of the series sometimes ergodicity is required. At least according to all my econometric books $\endgroup$ – RScrlli Feb 8 at 12:32
  • $\begingroup$ In OLS we need the erros to be iid, not the dependent variable. $\endgroup$ – Lucas Farias Feb 8 at 16:04
  • $\begingroup$ The ergodic-stationarity of the dependent and the independent variables allows us to proof the ergodicity and stationarity of the error term $\endgroup$ – RScrlli Feb 8 at 17:10

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