I want to simulate paths for a commodity price. I use the historic data in the following way:

  1. $X_t$ is the price.

  2. $\ln\left(\frac{X_t}{X_{t-1}}\right)$ is the daily return.

  3. I calculate the slope of the regression for six prices.

  4. I calculate the slope of the slopes found in step 3.

For the simulation I use the Ornstein-Uhlebeck equation How can I produce smoother paths in order to have a robust model, i.e. I want to calculate the slope of every six observations and then again the slope of the slopes?


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