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I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much smaller. Is this correct? Because most figures that I have seen, is that the peaks are approximately the same size.

Thanks in advance!

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    $\begingroup$ could you edit the post with the plot included, and add more information about what model/process was used to generate the conditional volatility time series if it's not the sample estimator. $\endgroup$ – develarist Jun 16 '19 at 4:20
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In my understanding that truly depends on how large the time frame you consider is. Indeed, on one side you have log-returns on the other conditional volatility, which are two different concepts.

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