Quote from: BTCtrader71 on January 02, 2017, 07:06:33 PM

Quote from: jbreher on January 02, 2017, 06:50:43 PM

Quote from: harrymmmm on January 02, 2017, 12:28:24 PM

Quote from: jbreher on January 02, 2017, 06:12:23 AM

Quote from: BTCtrader71 on January 02, 2017, 01:03:29 AM

Any curve can be represented as a sum of sinusoidal curves, i.e. a Fourier series.

Not quite. Any periodic curve can be represented as a sum of sinusoidal curves. The trick is in knowing the periodicity of $=f(t). protip: that f() ain't periodic.

Nope.
An infinite fourier series can match any continuous differentiable function.

An infinite series of a non-deterministic function is unrealizable.

Unless you know the function a priori, you cannot derive a convolution thereof. If you know the function a priori, there is no need to convolve it in order to profit. The entire concept of obtaining a Fourier series of $=f(t) is therefore nonsensical.

Obviously we don't know what the price curve is going to be in the future. That's not the point. The point is that if the price starts at f(t_0) = X and ends at the same price f(t_1) = X, and in between it has lots of ups and downs, then this method will increase the end-value of your total holdings (expressed in BTC or in $). It doesn't matter what f(t) does in between. You don't have to know ahead of time what f(t) is going to do. The demonstration of this statement makes use of the fact that f(t) = the sum of lots of sine waves, for any f(t). This is true even if we don't know ahead of time what exactly f(t) is.

There is a simple way to do a sanity check to determine if what is proposed is nonsensical.

1) Find a price level X where the curve hits at 2 points, t_0 and t_1. Solve for f(t_0) = X and f(t_1) = X.

2) Find another price level Y where the curve also hits at 2 points, t_2 and t3. Solve for f(t_2) = Y and f(t_3) = Y.

Use the 2 solutions to extrapolate 2 curves into the future. If the curves are wildly different then all this would be a waste of time.