Least-squares signal extrapolation (linear prediction)

Introduction

Least squares method can be used to find patterns (correlations) in a signal which can then be used to extrapolate the signal (see the lecture note).

Task

• Implement a function with the signature

  vector predict(vector x, int n)
  

  that takes the signal vector `x` and the number of terms `n` as input and returns the vector of coefficients `a_1,...,a_n` that can be used to extrapolate the signal using the "linear prediction" formula,

  `x_{k}=x_{k-n}a_1+x_{k-n+1}a_2+...+x_{k-1} a_n`