A stylized model of ‘Momentum’ processes: a research note

Abstract

Several phenomena of interest like stock price movements, online auction bid prices or inventory levels, can be stylized as ‘momentum processes’, whereby the very start of activity (‘up’ or ‘down’) can trigger subsequent activity in that direction. We calculate the transient probabilities of being in a particular state (eg, stock price or current auction bid level) in such activities. The calculations can be used to estimate the expected time to reach a certain price, inventory level or bid. The processes can be modified to show the phenomenon where the lack of activity can have an ‘inertia of rest’.

Keywords:

• momentum processes
• correlated random walk
• quasi-birth-death process
• transient analysis

Acknowledgements

We thank two anonymous reviewers for their detailed comments and suggestions on an earlier version of the note.