I am trying to model a wind turbine power curve, or in other words, given the windspeed (X), I would like predict the produced power (Y). I want to use historical data to estimate this model. You can read more about the power curve here: http://www.windpowerwiki.dk/index.php?title=Power_curves. On the given rescaled power curve below, the power can never go below 0 and never above 4, and the windspeed can never go below 0.
Question 1: What type of model would you use to predict Y with X (the red line on the plot is a LOESS fit)?
Question 2: Is it possible, in your suggested model, to use lagged variables of Y? The dots on the graph are measurements over time, so if one point is above the red line, it is very likely that the next measurement in time is also above the red line (this is because another important predictor, air pressure, is not included in the model, so I assume there is important autocorrelation). How can I take this into account?