NAG Library Manual, Mark 30.1
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NAG CL Interface Introduction
Example description

nag_tsa_multi_inputmod_estim (g13bec) Example Program Results

Parameters to g13bec
____________________

nseries......................   2

criteria............ Nag_Marginal    cfixed................. Nag_FALSE
alpha..................  1.00e-02    beta...................  1.00e+01
delta..................  1.00e+03    gamma..................  1.00e-07
print_level... Nag_Soln_Iter_Full
outfile................    stdout

Iter =  -1     Residual =   6.456655e+03     Objf =   7.097184e+03

phi                     0.000000e+00
stheta                  0.000000e+00
omega      series   1   2.000000e+00
delta      series   1   5.000000e-01
constant                8.688399e+01

Iter =   0     Residual =   5.802775e+03     Objf =   6.378435e+03

phi                     0.000000e+00
stheta                  0.000000e+00
omega      series   1   2.000000e+00
delta      series   1   5.000000e-01
constant                8.573272e+01

Iter =   1     Residual =   2.354664e+03     Objf =   2.498647e+03

phi                     6.589153e-01
stheta                  6.571389e-02
omega      series   1   3.721182e+00
delta      series   1   5.237968e-01
constant                5.739128e+01

Iter =   2     Residual =   1.922339e+03     Objf =   2.032375e+03

phi                     6.417690e-01
stheta                 -2.361191e-01
omega      series   1   4.523132e+00
delta      series   1   5.742824e-01
constant                3.814856e+01

Iter =   3     Residual =   1.530797e+03     Objf =   1.630603e+03

phi                     5.550797e-01
stheta                 -3.097333e-01
omega      series   1   7.697297e+00
delta      series   1   7.358370e-01
constant               -9.322197e+01

Iter =   4     Residual =   1.232926e+03     Objf =   1.324116e+03

phi                     3.698329e-01
stheta                 -2.145294e-01
omega      series   1   9.116523e+00
delta      series   1   6.923742e-01
constant               -9.985550e+01

Iter =   5     Residual =   1.200813e+03     Objf =   1.289272e+03

phi                     3.889281e-01
stheta                 -2.649652e-01
omega      series   1   8.906746e+00
delta      series   1   6.659905e-01
constant               -7.782515e+01

Iter =   6     Residual =   1.197922e+03     Objf =   1.286734e+03

phi                     3.752731e-01
stheta                 -2.499956e-01
omega      series   1   8.957172e+00
delta      series   1   6.616140e-01
constant               -7.656262e+01

Iter =   7     Residual =   1.197934e+03     Objf =   1.286623e+03

phi                     3.804046e-01
stheta                 -2.594526e-01
omega      series   1   8.954182e+00
delta      series   1   6.599012e-01
constant               -7.553429e+01

Iter =   8     Residual =   1.198009e+03     Objf =   1.286613e+03

phi                     3.807082e-01
stheta                 -2.567453e-01
omega      series   1   8.956063e+00
delta      series   1   6.597438e-01
constant               -7.549190e+01

Iter =   9     Residual =   1.197988e+03     Objf =   1.286612e+03

phi                     3.808772e-01
stheta                 -2.580559e-01
omega      series   1   8.955983e+00
delta      series   1   6.596508e-01
constant               -7.543851e+01

Iter =  10     Residual =   1.198002e+03     Objf =   1.286611e+03

phi                     3.809218e-01
stheta                 -2.575832e-01
omega      series   1   8.956106e+00
delta      series   1   6.596484e-01
constant               -7.544005e+01

Iter =  11     Residual =   1.197997e+03     Objf =   1.286611e+03

phi                     3.809235e-01
stheta                 -2.577863e-01
omega      series   1   8.956084e+00
delta      series   1   6.596411e-01
constant               -7.543552e+01



The number of iterations carried out is   11

The final values of the parameters and their standard deviations are

   i            para[i]                 sd
   1            0.380924            0.166379
   2           -0.257786            0.178178
   3            8.956084            0.948061
   4            0.659641            0.060239
   5          -75.435521           33.505341


The residual sum of squares =     1.197997e+03

The objective function =     1.286611e+03

The degrees of freedom =    34.00

The correlation matrix is 

    1.0000    -0.1839    -0.1775    -0.0340     0.1394
   -0.1839     1.0000     0.0518     0.2547    -0.2860
   -0.1775     0.0518     1.0000    -0.3070    -0.2926
   -0.0340     0.2547    -0.3070     1.0000    -0.8185
    0.1394    -0.2860    -0.2926    -0.8185     1.0000

The residuals and the z and n values are

   i         res[i]          z(t)        noise(t)

   1          0.397        180.567         -75.567
   2          3.086        191.430         -72.430
   3         -2.818        196.302         -77.302
   4         -9.941        195.460         -86.460
   5         -5.061        201.594         -84.594
   6         14.053        199.076         -64.076
   7          2.624        195.211         -69.211
   8         -5.823        193.450         -81.450
   9         -2.147        197.179         -81.179
  10         -0.216        196.217         -74.217
  11         -2.517        191.812         -76.812
  12          7.916        184.544         -69.544
  13          1.423        194.322         -72.322
  14         11.936        200.369         -62.369
  15          5.117        200.990         -65.990
  16         -5.672        200.468         -75.468
  17         -5.681        195.763         -80.763
  18         -1.637        184.025         -76.025
  19         -1.019        175.360         -75.360
  20         -2.623        175.492         -79.492
  21          3.283        182.162         -75.162
  22          6.896        183.857         -68.857
  23          5.395        190.797         -67.797
  24          0.875        194.327         -72.327
  25         -4.153        205.558         -77.558
  26          6.206        204.261         -68.261
  27          4.208        207.104         -67.104
  28         -2.387        196.423         -74.423
  29        -11.803        189.924         -87.924
  30          6.435        175.158         -72.158
  31          1.342        160.761         -71.761
  32         -4.924        156.575         -79.575
  33          4.799        164.256         -75.256
  34         -0.074        167.783         -73.783
  35         -6.023        184.483         -80.483
  36         -6.427        193.055         -85.055
  37         -2.527        199.390         -80.390
  38          2.039        201.302         -75.302
  39          0.243        195.695         -76.695
  40         -3.166        183.738         -80.738