--------------- --------------- --------------- -- --------------- --------------- ---------------
                                     b=0.2                                              b=0.3      
   $T$   $a_2$   $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$      $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$
   50     0.0        0.014           0.050           0.082              0.012           0.052           0.102
          0.2        0.014           0.062           0.124              0.008           0.064           0.130
          0.5        0.044           0.144           0.234              0.046           0.124           0.226
          0.8        0.074           0.362           0.468              0.098           0.262           0.372
          1.0        0.150           0.372           0.512              0.154           0.336           0.464
                                     b=0.1                                              b=0.2      
         $a_2$   $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$      $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$
   100    0.0        0.004           0.046           0.100              0.014           0.050           0.084
          0.2        0.012           0.074           0.126              0.022           0.076           0.130
          0.5        0.056           0.190           0.296              0.076           0.222           0.330
          0.8        0.164           0.402           0.554              0.210           0.412           0.574
          1.0        0.330           0.572           0.688              0.366           0.624           0.730
                                    b=0.06                                              b=0.1      
         $a_2$   $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$      $\alpha=0.01$   $\alpha=0.05$   $\alpha=0.10$
   200    0.0        0.008           0.055           0.106              0.014           0.048           0.098
          0.2        0.016           0.088           0.144              0.024           0.100           0.186
          0.5        0.126           0.280           0.428              0.174           0.392           0.502
          0.8        0.394           0.646           0.752              0.448           0.710           0.810
          1.0        0.636           0.864           0.926              0.692           0.888           0.952
  ----- ------- --------------- --------------- --------------- -- --------------- --------------- ---------------

  : Empirical size and power of the bootstrap studentized test for the equality of two spectral density operators. The functional time series in each group were generated according to models (\[mod-1\]) and (\[mod-2\]).[]{data-label="tab:empsize-power"}

A Real-Life Data Example
------------------------

We applied the bootstrap studentized test to a data set 