It seems like you are comparing the intercept (5.047) with the mean (8.57):
for ARIMA estimation the right representation is
x_t - 8.57 = 0.45 * (x_{t-1} - 8.57) + e_t

Indeed 5.047 / (1 - 0.414) = 8.61 which is very close to 8.57.
Best,
Matteo



Il 23/02/2019 10:48, Raul Gimeno ha scritto:

Hello

 

I simulated the following AR(1) process xt = 5 + 0.4xt-1 + e  with  e = N(0,1)   200 observations

Estimation with OLS: xt = 5.047xt + 0.414xt-1

Estimation with gretl ARIMA: xt = 8.57 + 0.43xt-1

 

I simulated this AR(2) process: xt = 5 + 0.4xt-1 -0.1xt-2 + e

OLS estimation: xt = 4.64 + 0.377x t-1 -0.0075 x t-2

ARIMA estimation: xt  = 7.36 + 0.369xt-1 -0.0076xt-2

 

Why is gretl giving such a bad estimation compared to OLS-estimation?

 

Thank you

Raul


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-- 
Matteo Pelagatti
Department of Economics, Management and Statistics
University of Milano-Bicocca
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