A Complete Introduction To Time Series Analysis (with R):: Durbin-Levinson Algorithm

The equations of the Durbin-Levinson Algorithm

In the last article, we saw how we could find the form of the best linear predictor of X_{n+h} using all previous observations up to n has the form

where the coefficients satisfy

The coefficients of the best linear predictor satisfy this equation.

We also saw that in practice it is very cumbersome to invert the Gamma matrix on the left. Therefore, we would like to have a way to find the coefficients without actually having to inverse the matrix by hand.

Dubin-Levinson Algorithm

Let {X_{t}} be a stationary time series and zero-mean , then for n=0,1,.. , the Dubin-Levinson algorithm computes coefficients

Let

Then, the Dubinson algorithm is given by