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Is recursive least square to estimate coefficients of ARMA(p,q) is equivalent to newton's method of finding coefficients using this -

$$C_{m+1}=C_m+(X^TV_mX)^{-1}X^T(Y-P_m)$$

EDIT:

I've used that equation in logistic regression to find coefficients. How to determine coefficients of ARMA(1,1) using following dataset -

$$ \begin{matrix} Period & Value \\ 1 & 15 \\ 2 & 12\\ 3 & 19 \\ 4 & 21 \\ 5 & 17\\ \end{matrix} $$

Here I've found a MATLAB function which uses Recursive Kalman Filter to estimate coefficients and here the process has been explained. It outputs $ar$ and $ma$ coefficients only and they are very different from those produced by R.

For a given 100 observations, it outputs - $$ar: 0.9616\,\,\,\,ma: -179.4289\,\,\,\,\sigma: 0.0012 \,\,\,\, LL: -160.2952$$

with the same R (setting include.mean = FALSE) produced - $$ar: 0.9590\,\,\,\,ma: 1.0000\,\,\,\,\sigma^2: 0.01309\,\,\,\, LL: 70.66$$

  • No. In an ARMA model, you are modeling error terms, and what the error term is depends on what the form of the equation is. So, in contrast to a typical Newton's method problem, where you are finding a solution to $y=f(x)$, the $y$ is changing as you fit the terms, so the iteration is nonlinear. – Paul Apr 26 '17 at 18:18
  • @Paul yes it worked in non-linear logistic regression –  Apr 26 '17 at 18:44
  • In a logistic regression, non-linear or not, the target (Y) does not change. For a ARMA model, it does. – Paul Apr 26 '17 at 18:46
  • @Paul have a look at last section. Is he correct implementing kalman filter? Function itself is explanatory, no need to read explanation in second link. –  Apr 30 '17 at 01:53

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