We fitted AR(2) models to the mean corrected lake data using the Yule–Walker equations and Burg’s algorithm. If instead we fit an ARMA(1,1) model using the innovations method in the option...

We fitted AR(2) models to the mean corrected lake data using the Yule–Walker equations and Burg’s algorithm. If instead we fit an ARMA(1,1) model using the innovations method in the option Model>Estimation>Preliminary of ITSM (with the default valuem= 17), we obtain the modelX_t
− 0.7234X<sub>t

−1</sub> =Z_t
+ 0.3596Z<sub>t

−1</sub>
,{Z_t
} ∼ WN(0,0.4757),for the mean-corrected seriesX_t
=Y_t
− 9.0041. The ratio of the two coefficient estimates
and
to 1.96 times their estimated standard deviations are given by ITSM as 3.2064 and 1.8513, respectively. The corresponding 95% confidence intervals are therefore