I was conducting some time-series analysis on Bitcoin/USD when I stumbled on this algorithm, which produced the following prediction:

I don't claim the algorithm has much skill (based on this dataset, it seems to perform almost as well as a simple exponential trendline, which is not surprising since the algorithm is just noise added to an exponential trendline). But I am impressed at how natural the price movements predicted seem. The chart looks nice

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The algorithm is fairly simple:
- 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?