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I am reading the following paper. In particular, in section 4 - numerical determination of OTRs, it mentions applying Ordinary Least Square on Eq(5). However, what I don't know is whether ${P_{0,0}, P_{0,1}, ...,P_{0,T_1}}$ is simulated or coming from actual historical data? I am guessing it's coming from actual historical data because we need to first estimate the parameters then generate simulated price series.

Furthermore, where do I get the forecasted prices ${E_0[P_{0,T_0}], ..., E_0[P_{1,T_1}]}$? Am I suppose to predict them from my own strategy? What if my strategy only predicts direction but not actual price movement?

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