Levinson-Durbin and Autocovariance

As discussed, I am implementing estimation methods for phi in AR modelling. We covered yule_walker earlier, I’ll write a post about that. After it’s implementation, we go ahead with another estimation method - Levinson Durbin

Levinson-Durbin requires timeline series to be demeaned(series = series - series.mean) and it’s autocovavirance.

Autocovariance of series is represented by summation of summation of product of series with series at lag k. That is, summation of (x_i * x_{i+lag}). It is also directly related with acf of series as acf(k) = acvf(h) / acvf(0). It’s code can now be found in Statsample::TimeSeries’s acvf method.

Now, with the help of autocovariance series, our levinson_durbin function recursively computes the following parameters:

• sigma_v : estimation of error variance
• arcoefs : AR phi values for timeseries
• pac : unbiased levinson pacf estiation
• sigma : sigma for AR.

L-D performs recursive matrix and vector multiplications to populate it’s toeplitz matrix. Here is some code depicting those manipulations:

Implementation can be found here.

Now, in this week, I will integrate this in AR modelling and perform some tests to verify the estimation. And will soon start with next estimation method :)

Cheers,
Ankur Goel