I'm looking for a function [math]h: R^m \to R[/math]

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I'm looking for a function
[math]h: R^m \to R[/math]
so that for m consecutive components of a vector [math]v \in R^n [/math] with [math]m<n[/math], the function [math]h[/math] approximates the next component. For starters, this h can be a linear form w.

I.e. I'm looking for the constant [math]w \in R^m, c\in R[/math] so that [math]w \, \cdot \, (v_k,v_{k+1},v_{k+2},...,v_{k_m}) + c \sim v_{k+m+1} [/math].

Yes more concretely, I'm interested if there can be a simple predictor for this price data (BTC-USDT), at least for the sign (up, down)

https://pastebin.com/pX6Ymm2s


v = [4206.001, 4215.0, 4218.518, 4235.0, 4222.15, 4220.0, 4220.1, 4220.1, 4210.1, ..... 4220.00004221, 4220.00048457, 4220.0, 4220.0, 4225.0, 4234.0, 4227.0, 4230.0, 4235.231, 4231.1, 4239.0, 4243.99999999, 4247.72834495, 4250.00000001]

So let's say we're interested in an estimator w of length m=4, then

w_1 · 4206.001 + w_2 · 4215.0 + w_3 · 4218.518 + w_4 · 4235.0
should evaluate to roughly 4222.15
and if we plug in four components of v shifted by an index, it should yet estimate the next component.

The 4th component will be like the 0'th approximation, and minus difference of the 4th and 3rd will indicate the direction in which it is goin, and so on.