;;; 20 point time series from page 287 (first row is X_1, X_2, X_3, X_4;
;;; second row is X_5, X_6, X_7, X_8; etc)
 71.0  63.0  70.0  88.0 
 99.0  90.0 110.0 135.0
128.0 154.0 156.0 141.0
131.0 132.0 141.0 104.0
136.0 146.0 124.0 129.0

sample mean = 117.4

p = 1
\phi_{1,1} = 0.7415951139732189
innovations variance = 352.21671265971565

p = 2
\phi_{1,2} =  0.7557426273700377
\phi_{2,2} = -0.01907713943936502
innovations variance = 352.0885278781919

p = 3
\phi_{1,3} =  0.7564278899100625 
\phi_{2,3} = -0.046223877768903764
\phi_{3,3} =  0.03592061284674202
innovations variance = 351.6342314211136

p = 4
\phi_{1,4} =  0.7658252885356229
\phi_{2,4} = -0.058316772933774776
\phi_{3,4} =  0.23381407427807
\phi_{4,4} = -0.2616157654563174
innovations variance = 327.56739697517594

;;; for the fitted AR(4) model, here are the corresponding estimated
;;; acvs for lags 0 to 20 (note that the values for lags 0 up to 4
;;; correspond to the usual biased estimates for the acvs)

lag  0 Yule-Walker acvs estimate = 782.64
lag  1 Yule-Walker acvs estimate = 580.402
lag  2 Yule-Walker acvs estimate = 423.704
lag  3 Yule-Walker acvs estimate = 321.786
lag  4 Yule-Walker acvs estimate = 152.678
lag  5 Yule-Walker acvs estimate = 45.38479733331212
lag  6 Yule-Walker acvs estimate = -9.756413326328783
lag  7 Yule-Walker acvs estimate = -58.60442844194004
lag  8 Yule-Walker acvs estimate = -73.64315824396786
lag  9 Yule-Walker acvs estimate = -67.13473700910302
lag 10 Yule-Walker acvs estimate = -58.26895664759184
lag 11 Yule-Walker acvs estimate = -42.595723788941825
lag 12 Yule-Walker acvs estimate = -25.65366011821324
lag 13 Yule-Walker acvs estimate = -13.22277305623658
lag 14 Yule-Walker acvs estimate = -3.345697349214449
lag 15 Yule-Walker acvs estimate = 3.3544159078859703
lag 16 Yule-Walker acvs estimate = 6.383738290194124
lag 17 Yule-Walker acvs estimate = 7.370224273239524
lag 18 Yule-Walker acvs estimate = 6.931621937533915
lag 19 Yule-Walker acvs estimate = 5.493643448273032
lag 20 Yule-Walker acvs estimate = 3.8561168426989134