Exact MLE Mean-Zero AR(1)
This function is used by GetFitAR in the AR(1) case. It is a fast exact solution using the root of a cubic equation.
AR1Est(z, MeanValue = 0)
z |
time series or vector |
MeanValue |
known mean |
The exact MLE for mean-zero AR(1) satisfies a cubic equation. The solution of this equation for the MLE given by Zhang (2002) is used. This approach is more reliable as well as faster than the usual approach to the exact MLE using a numerical optimization technique which can occasionally have convergence problems.
MLE for the parameter
A.I. McLeod and Y. Zhang
Zhang, Y. (2002). Topics in Autoregression, Ph.D. Thesis, University of Western Ontario.
AR1Est(lynx-mean(lynx))
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