Use date numbers...example for an axes...
For the selection, convert the requested time ranges into date numbers, too, and use the logical operations to select between, inclusive or not, etc., ...
NB: When generating series of date numbers, always use integer multiples of the smaller time granule such as seconds above rather than dividing out the fraction of an hour or day and using floating point deltas. The latter will end up with floating point comparisons that do NOT compare owing to that rounding whereas the rounding will be consistent inside datenum and friends if use the integer deltas. As can be seen in the above example, the functions are "smart enough" to know how to wrap times when building the vector.
In your case, you'll be reading a time vector, presumably as string; simply convert it or ignore it and just build the time history as shown.
The example does not use the newer timeseries class; I don't have it in the version installed here. If choose to use it, some of the machinations are a little different but the ideas are the same. One thing you do have to be aware of is that there's a whole different set of formatting abbreviations between the two.