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Question:
how can the initial values $\left(a[0],\,\dots,\,a[k-1]\right)$ and the coefficients $\left(c_k,\,\dots,\,c_0\right)$ be determined that solve

  • $\min\limits_{a[0],\dots,a[k-1]\\ c_k,\dots,c_0} \left\|\left(x[0]-a[0],\,\dots,\,x[N]-a[N]\right)\right\|$
  • $n\ge k\implies a[n]=c_0+\sum\limits_{i=1}^k c_ia[n-i]$

i.e. how to find for a given sequence the best approximating linear recursion with given depth $k$

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  • $\begingroup$ What norm is this? L2? $\endgroup$ Commented Apr 30, 2024 at 9:07
  • $\begingroup$ @CommandMaster you may assume the Euclidean norm, which is easier to handle, but I don't want to rule out sum norm or maximum norm $\endgroup$ Commented Apr 30, 2024 at 10:12

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