First thanks for help. I benefited a lot from the forums.I am trying to analyze the spread between two stocks. Most time the volatility of the spread (from empirical study) is stable, sometimes it has a spike. Is that because the volatility changes or the drift changes? How can I differentiate them?

A spike in spread volatility is most likely caused by a data error. It could simply be a wrong price for one security, or more likely, a non-contemporaneous quote. It could also be a sharp event of some sort that affected only one security, or both securities but not in the way they are usually related. Generally spread volatility moves up and down, maybe staying near one level for a while, then shifting to another. True spikes in volatility are not common.

more common than you think! Check out Sornette´s work on this ...

If your interested in the volatility of the spread, doesn't the problem boil down to modelling the distribution and stability of correlation?

yes. I tried GARCH model, the predictability is so low that I gave up on it. Any suggestions on how to model it?

Thanks for both of your insight. I did find some spike in the pairs I tested. I agree that it might be caused by some events in one company, then it should be a drift change instead of volatility change in spread. How can you differentiate these two situation or you always assume one is constant?

I'd start by looking at the events more closely. Are they caused by one underlying making a large move or both? I'd look for data errors: bad prices, missing data or non-contemporaneous moves.If there is only one large move by one or both underlyings, and there was nothing unusual about option prices before the move, I'm inclined to call that a jump in the underlying(s) rather than a volatility spike in the spread.Calling it a volatility spike only makes sense if (a) you can see it in option implied volatilities or (b) it persists for more than one move. But if it persists for long, it's not a spike. I think you need at least three moves to call it a volatility spike, and you can't have many small moves in between, nor can it persist for more than about ten or so observations. If this happens and all the moves are in the same direction (for each underlying), I suspect it is a single move that took place over more than one observation period. If the moves offset, I suspect it was a data error or trading error. Only if the moves are in different directions, but don't offset completely (i.e. there is significant net movement) does the volatility spike analysis make sense.

Thanks for your advice. I am always impressed by your depth.

Thanks for the kind words. I'm not so impressed with my depth, I have to lose some weight.