- Treat the logarithm of the time series as a function with domain [0, π).
- Detrend the dataset.
- Fit the function as a linear combination of sin(x), sin(2x), sin(3x), etc. to the desired precision.
- Extrapolate this to the domain [π, 2π).
- Retrend the dataset and remove the logarithm to get predicted price values.
- Multiply by the "depression factor" to correct predicted price values so as to be consistent with today's price.
Since this algorithm has no skill, I feel comfortable sharing it as a curiosity. Does anyone else have any similar failed models that nevertheless produce interesting results?
You mean you changed the entire domain available at the time to [0, π)? Or do you change every year to [0, π), or something like that?
If it's the first, how do you refit the model as more data becomes available? Do you set the entire domain to [0, π) every time?
The "depression factor" bothers me. You mean, your model yields an expected price, which you have to change to current price?
Instead of doing that, try creating a model for the differences in price. That way, you won't need any depression factor. See the first model in my signature for an example.