WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS Lorenzo Sabatelli 1,2, Shane Keating 1, Jonathan Dudley 1 and Peter Richmond 1 1 Department of Physics, Trinity College Dublin 2, Ireland and 2 Hibernian Investment Managers, IFSC, Dublin 1, Ireland The authors acknowledge support from the EU via Marie Curie Industrial Fellowship MCFH

Objective waiting time distribution (WTD) for the Irish stock market 1850 to –10 stocks out of a database of 60 are examined. –waiting time distributions vary from a day to some months are compare with WTD for Japanese yen currency returns –waiting times vary from a minute to over an hour

19 th century Irish Stock Exchange Deals done 'matched bargain basis' members of exchange bring buyers and sellers together –Essentially same as today –Today, many more buyers and sellers. Recent studies of 19 th century markets find they were well integrated Dublin traded international shares –Not solely a regional market. World trends reflected in the Irish market –No exchange controls. –From 1801 to 1922 Ireland was part of UK Largest shares: Banks and key railways – –Quality investments for UK investors –Also traded in London.

Random walks Time

Markovian Random walk Continuous time random walk Montroll & Weiss 1965

Fourier Laplace Transform

Choice for memory function Ф

Results: Irish Stock Market data

Results: Yen Currency Market data

Conclusions: Irish data, –outside the cut off regime, survival time distribution exhibits two clear regions –can be well fitted by Mittag Leffler function –power law tail has exponent of magnitude less than unity (~ 0.4) Japanese yen –short waiting times (1 to 30 minutes) fits power law over large range –but exponent greater than unity (~ 1.9) –larger values of time shows a smaller power law regime having an exponent between 0.9 and 1.1 that is at the border of the regime that can be fitted with a Mittag Leffler function. –for larger waiting times, data exhibit two ‘humps’. The characteristic time could be associated with opening and closing of the major global trading centres.