Synchronising time series and video display

Use TimeSeriesShift to adjust your time series first. I have not handled that aspect of the question below, but rather the way to get the time out of a video stream and use it for live plotting, which is kind of non-trivial and worth answering here:

This video stream player is straight out of the documentation:

stream = VideoStream["ExampleData/bullfinch.mkv"];
Panel@Column[{
   Dynamic[stream["CurrentFrame"]],
   Slider[
    Dynamic[QuantityMagnitude[stream["Position"], 
      "Seconds"], (stream["Position"] = #) &], {0, 
     QuantityMagnitude[stream["Duration"], "Seconds"]}],
    Button[
    Dynamic[If[stream["Status"] === "Playing", "Pause", "Play"]],
    If[stream["Status"] === "Playing", VideoPause[stream], 
     VideoPlay[stream]]
    ]
   }, Alignment -> Center]

I generate a random time series:

(* example time series *)
ts = RandomFunction[WienerProcess[0, 1.5], {0, 50, .05}];

... and I create a dynamic plot. The ImagePadding is important to stop it jumping around. I also plot only a 2 second window so that the plot scrolls horizontally:

Dynamic[
 With[{t = QuantityMagnitude[stream["Position"], "Seconds"]},
  DateListPlot[ts, PlotRange -> {{t - 2, t}, {-10, 10}},
   AspectRatio -> 1, ImagePadding -> 20
]]]