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The Innovation Algorithm

  • To: mathgroup at
  • Subject: [mg36799] The Innovation Algorithm
  • From: "Dr.Robert Volèjak" <robert.volcjak at>
  • Date: Thu, 26 Sep 2002 04:56:54 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Hi there!

I need to program the following recursion scheme for time series
forecasting (The Innovation Algorithm).
I will write it in "pseudo"-Mathematica notation. K is the given m x m
autocovariance (numerical) matrix of the process

v[0] = K[[1,1]];

H[n,n-k] = (v[k])^(-1) (K[[n+1,k+1]]  - Sum[(H[k,k-j] H[n,n-j] v[j]),
{j,0,k-}])        for k=0,1,...,n-1

v[n] = K[[n+1,n+1]] -Sum[(H[n,n-j])^2 v[j],{j,0,n-1}]

The scheme should be solved in the order v[0], H[1,1], v[1], H[2,2],
H[2,1], v[2], H[3,3], H[3,2], H[3,1], ...

I have already tried to program it in a straght-forward  way, but as
have no experience with recursive functions with two variables, it
doesn't seem to work properly and is also very slow. Any help would be
greatly appreciated. Thank you.


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