of data $X[~,i:i+w-1]$ to update the wavelet coefficients.

    (b) Update the transformed coherence at the set of discriminative indices using the wavelet coefficients calculated in the previous step.

    (c) Apply dynamic classification method to obtain the probability that the signal belongs to a particular class for window $i$, denoted $p_{t,i}^{(c)}$ for $t=i,i+1,\hdots,i+w-1$.

5.  Average probability estimates for each window using to obtain the final probability that the signal $X$ belongs to a particular class $c$ over time, $p_{t}^{(c)}$ for $t=1,2,\hdots,T$.

Synthetic Data Examples {#sec:examples}
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We now turn to assess the performance of our proposed online dynamic classification approach. To this end, a simulation study is designed to test the ability of this wavelet-based appproach to classify data streams exhibiting various characteristics. More specifically, the study consists of three different scenarios. These scenarios are chosen to mimic signals arising in practice:

Scenario 1: Signal of length 1024, short time segments of length 100 between changes in class, nine class changes in total.

Scenario 2: Signal of length 1024, alternating long/short segments of length 300 and 100 between changes, five class changes in total.

Scenario 3: Signal of length 2048, long segments of length 300 between changes, six class changes in 