This actually may be in the wrong place, since I am not presenting this as an actual theory on how time traveling would work. Its more a counter to its use in Hollywood x.x if it should go somewhere else because of that, tell me and I'll move it, or a Siren can just do it.
With that clarified, this is how my own brand of time travel works. I give you my blessing if you'd like to use it in your writing :)
Picture that this is Time.
The start is obviously the start, where as the end is not the future, but the present. Time does not extend past the present. This means that when you travel back, you are not just crossing a distance of time, you are slicing that part off and starting a new present. You want to travel to here...
You do that, and Time resembles this...
What was between X and the Present is GONE. Time Travel can NOT be used to correct mistakes. You cannot use it to stop John Connor from defeating you Skynet, because when you push that button, your time period is erased forever.
And no, events will not carry out in a similar, but precarious fashion, threatening to repeat events if you don't intervene. Life is chaos. It is an endless succession of random events piled one atop the other. If you throw a hand full of sand at a glass floor, the spread of sand will ALWAYS be different. To expect the random actions of human thought, physics, and the universe in general, to play out even remotely similar when simulated twice, is impossible. Identical futures do not happen.
So this should make traveling forward impossible, right? If the Present is the end of time, and time is growing constantly, then theres no Future to travel to. This is still accurate, but forward jumps are possible. When you travel forward, you are actually not traveling at all. You are staying still, displaced from time all together for a certain period. When the designated time comes, you re-enter Time. This is the blink of an eye to you, but really, you have been a temporal figment frozen for hundreds of years.
So, forward jumps cause no negative effects, but backward jumps are permanent. Are there any other risks or factors? Yes. While its still true that going back means your future is gone, it actually splits the time stream in two.
What you've done when returning to X is split off to start a new timeline. The original still exists, but is inert. Its a figment, a ghost. The basic fundamental laws of space, time, physics, matter, the building blocks that make reality possible, remain on the main Time Stream, while the new Splinter Stream forks off, using the Main as its foundations but otherwise completely new and fresh, with infinite possibilities.
So... what happens if you go back twice? Or three times? Lets go back to half way during this new Splinter Stream...
Okay, we now have a second inert Time Stream, and a new one branching off. Its attached to the inert stream, not the Main, and so has to obtain its fundamentals through the dead Stream. Not too tough. The Stream can handle it. But what if we travel back past the point of the Split... Lets go back just before the very first Split.
Look at that... only three jumps, and look at how much dead weight you've left on the Time Stream. With only the straight line representing Time, and the x's representing dead Time, there is only ever one Split in your time. Traveling to a point after it means the new Splinter Stream has to dig through more dead layers to get its fundamentals. Traveling to a point before the Split kills the entire Splinter Stream, but then your new one should have clean and complete access to the Main Stream, right? Yes and no... lets have a look at a Time Stream with multiple Splits without shortening it. The Time Stream is 1000 years long.
The people in this Time Stream first traveled back from the year 1000 to the year 500, half way back. This created a Splinter that went on towards the year 750. For whatever reason, another jump occurred to shortly after the first. This one lasted 50 years longer then the last, before needing to be scaled back to around the year 300. That reality lasted until 550, then went back to 250. That is their current Stream... now look at the straight line. It stretches 800 years, with another 200 to reach the Main Streams end. After that, it will be completely free of the dead Splinters.
But from the year 500 to the year 750, it runs parallel to Stream #2. From 550 to 750, it runs parallel to # 2 and #3. From 750 to 800, it runs next to #2 again. From 350 to 550, it also has #4. Look at 500 to 550. A very small window, but there are three dead Splinter Streams here, 50 years worth of events. While normally, these do not influence a current Streams events, having to sift through so much constantly to reach the Main Stream will cause a higher probability of similar events. The more dead Streams parallel, the more the events are imposed.
Very large events, like wars, or natural disasters, are impossible to repeat like this, because of how many factors are involved. However, if running parallel to both a time of war and a time of depression, similar tones can be imposed on the Streams. Or, if in one dead Stream a box were to fall, and in the main Stream, there is a box that so happens to be in a similar place, with the potential to fall, it will.
In other words, the dead Streams will NOT impose great change on the current Stream, but if they do cross in a small way, then the crossing events can happen similarly or even identically.
This is only 5 instances of Time Travel. Perform dozens, and keep going, you run parallel to more and more dead Streams, and the probability for 'bleeding over' increases. There is only one possible fix for this, and that is traveling forward past the time of the Original Stream, where no dead Streams can influence your time. The time between your jump and your arrival happen as per normal, however, so the new world you go to will still have suffered Bleed Over.
I hope I've made sense of all this ^^ I'm sure theres some holes in it somewhere, so if you see inconsistencies and have suggestions, please share :)