As far as I can tell, the spec does not specify behavior for negative values of timestamps in TextTrackCues.
http://www.whatwg.org/specs/web-apps/current-work/#texttrackcue

Negative time values are not allowed in WebVTT (a '-' would constitute a malformed timestamp and the entire cue would be dropped on the floor).  However, negative time values could be specified via:

(a) var cue = TextTrackCue('cue1', -3, 3, 'This cue starts before the video itself!')");

or

(b) cue.startTime = -1000;

Should this be allowed?

I can think of a few options:

(1) Throw an error and drop the cue.
    - In the case of (a), should the constructor return null? an empty cue?
    - In the case of (b), should the cue maintain it's original startTime?  Should it be removed from the track it is associated with?

(2) Set the time value to 0 (or to the startTime of the media) rather than allowing the negative value.
    - Should we also throw an error in this case to notify authors that the value was not accepted?

(3) Allow negative timestamps to exist and just never render that cue (or render it if the time span does in fact overlap the video, e.g. -5 --> 5 would be rendered from 0 to 5).
    - I suppose authors could use negative timestamps to force cue ordering for cues that all start at 0.
    - Should the enter, exit, and cuechange events fire at 0 or not at all?

What are your thoughts?