Yule Walker Equation in Matrix Form

 

• If we write and above equation for k=1, 2, . . ., n and use the fact that ρ(k) = ρ(-k), we can write it in a matrix form.
• Using the data we have we can estimate values of ρ  (auto correlation coefficients)
• acf() routine in R gives us that
• Using values of ρ we can then estimate values of Φ (parameters of AR process)

 

• Above is an example for AR process
• We can solve these equation for values of Φ1, Φ2 and Φ3

 

Reference:

• https://www.coursera.org/learn/practical-time-series-analysis/home/week/4