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Luc Bauwens · W<strong>in</strong>fried Pohlmeier · David Veredas<br />

Editor’s <strong>in</strong>troduction: <strong>recent</strong> <strong>developments</strong><br />

<strong>in</strong> <strong>high</strong> <strong>frequency</strong> f<strong>in</strong>ancial econometrics<br />

“But there are several aspects <strong>of</strong> the quantitative approach to f<strong>in</strong>ance,<br />

and no s<strong>in</strong>gle one <strong>of</strong> these aspects, taken by itself, should be confounded<br />

with f<strong>in</strong>ancial econometrics. Thus, f<strong>in</strong>ancial econometrics is by no<br />

means the same as f<strong>in</strong>ance statistics. Nor is it identical with what we<br />

call general f<strong>in</strong>ancial theory…Not should be f<strong>in</strong>ancial econometrics a<br />

synonymous with the application <strong>of</strong> mathematics to f<strong>in</strong>ance. Experience<br />

has shown that each <strong>of</strong> these three view-po<strong>in</strong>ts, that <strong>of</strong> statistics, f<strong>in</strong>ancial<br />

theory, and mathematics, is a necessary, but not sufficient, condition<br />

for a real understand<strong>in</strong>g <strong>of</strong> the quantitative relations <strong>of</strong> modern f<strong>in</strong>ancial<br />

life. It is the unification <strong>of</strong> all the three that is powerful. And it is this<br />

unification that constitutes f<strong>in</strong>ancial econometrics.”<br />

This paragraph is a virtual copy <strong>of</strong> the one <strong>in</strong> p. 2 <strong>of</strong> Frisch’s Editor Note on<br />

Econometrica Vol. 1, No. 1. The only difference is that economics has been replaced<br />

by f<strong>in</strong>ance, economic by f<strong>in</strong>ancial, econometrics by f<strong>in</strong>ancial econometrics.<br />

It was written 74 years ago but it fully reflects the spirit <strong>of</strong> this special issue.<br />

High <strong>frequency</strong> f<strong>in</strong>ance is an archetypical example <strong>of</strong> Ragnar Frisch’s words.<br />

It represents a unification <strong>of</strong> (1) f<strong>in</strong>ancial theory, <strong>in</strong> particular market microstructure,<br />

(2) mathematical f<strong>in</strong>ance, exemplified <strong>in</strong> derivative markets, and (3) statistics,<br />

for <strong>in</strong>stance the theory <strong>of</strong> po<strong>in</strong>t processes. It is the <strong>in</strong>tersection <strong>of</strong> these three components<br />

that yields an <strong>in</strong>credibly active research area, with contributions that enhance<br />

the understand<strong>in</strong>g <strong>of</strong> today’s complex <strong>in</strong>tra-daily f<strong>in</strong>ancial world.<br />

“Theory, <strong>in</strong> formulat<strong>in</strong>g its abstract quantitative notions, must be <strong>in</strong>spired<br />

to a larger extent by the technique <strong>of</strong> observations. And fresh statistical<br />

and other factual studies must be the healthy element <strong>of</strong> disturbance<br />

that constantly threatens and disquiets theorists and prevents them from<br />

com<strong>in</strong>g to rest on some <strong>in</strong>herited, obsolete set <strong>of</strong> assumptions.”<br />

Here aga<strong>in</strong> <strong>high</strong> <strong>frequency</strong> f<strong>in</strong>ance is fully reflected <strong>in</strong> Ragnar Frisch’s<br />

words. Its modus vivendi is a perfect comb<strong>in</strong>ation <strong>of</strong> observed real facts, market<br />

microstructure theory, and statistics and they all form a system <strong>in</strong> which each

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