Joint Extremal Behavior of Hidden and Observable Time Series

Details Joint Extremal Behavior of Hidden and Observable Time Series Joint Extremal Behavior of Hidden and Observable Time Series

2011-07-03

arxiv.org/abs/1107.0493v1

Mathematics

Probability

Scientific paper

We analyze the joint extremal behavior of two real-valued processes (X_t) and (Y_t) which can be interpreted as an observable and an unobservable time series. Our analysis is motivated by the well-known GARCH model which correspondingly represents both the observable log returns of an asset as well as the hidden volatility sequence. In particular, we study the behavior of (Y_t) under an extreme event of the observable process (X_t) where our results complement the findings of Segers (2007) and Smith (1992) for a single time series. We show that under suitable assumptions their concept of a tail chain as a limiting process is also applicable to our setting. Furthermore, we discuss existence and uniqueness of a limiting process under some weaker assumptions. Finally, we explore connections of our approach with the notion of multivariate regular variation.

Affiliated with

Also associated with

No associations

Rating

Joint Extremal Behavior of Hidden and Observable Time Series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Joint Extremal Behavior of Hidden and Observable Time Series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Joint Extremal Behavior of Hidden and Observable Time Series will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-3111