A Complete Introduction To Time Series Analysis (with R):: Innovations Algorithm
In the last article, we studied in depth the famous Durbin-Levinson algorithm, which allowed us to recursively compute the coefficients of the best linear predictor given by
satisfying the following
, without having to explictly invert the Gamma matrix. In this short article, we will take a look at the Innovations algorithm, another algorithm that will allow us to iteratively make predictions.
Innovations algorithm
We will now take a look at the Innovations algorithm. First, we are going to re-define the BLP of X_{n} as follows:
Next, we define the MSE as you might expect:
We define the one-step innovations as (prediction errors) as
That is,
At this point, you can already see that each “innovation” is definininf the difference by adding one prediction at the time. In order to…
