# A Primer for Unit Root TestingBrownian Motion: Differentiation and Integration

A Primer for Unit Root Testing: Brownian Motion: Differentiation and Integration [It was noted in Chapter 6 that Brownian motion is not differentiable along its path, that is with respect to t, see property BM6. However, even just a passing familiarity with the literature on random walks and unit root tests will have alerted the reader to the use of notation that corresponds to derivatives and integrals. In particular, the limiting distributions of various unit root test statistics invariably involve integrals of Brownian motion. Given that these are not conventional integrals, what meaning is to be attributed to them? This chapter is a brief introduction to this topic, starting by a contrast with the nonstochastic case. As usual, further references are given at the end of the chapter.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Primer for Unit Root TestingBrownian Motion: Differentiation and Integration

Part of the Palgrave Texts in Econometrics Book Series
Springer Journals — Nov 12, 2015
23 pages

/lp/springer-journals/a-primer-for-unit-root-testing-brownian-motion-differentiation-and-ssQ7rrHGwS
Publisher
Palgrave Macmillan UK
© Palgrave Macmillan, a division of Macmillan Publishers Limited 2010
ISBN
978-1-4039-0205-4
Pages
181 –204
DOI
10.1057/9780230248458_7
Publisher site
See Chapter on Publisher Site

### Abstract

[It was noted in Chapter 6 that Brownian motion is not differentiable along its path, that is with respect to t, see property BM6. However, even just a passing familiarity with the literature on random walks and unit root tests will have alerted the reader to the use of notation that corresponds to derivatives and integrals. In particular, the limiting distributions of various unit root test statistics invariably involve integrals of Brownian motion. Given that these are not conventional integrals, what meaning is to be attributed to them? This chapter is a brief introduction to this topic, starting by a contrast with the nonstochastic case. As usual, further references are given at the end of the chapter.]

Published: Nov 12, 2015

Keywords: Brownian Motion; Multiplicative Noise; Deterministic Function; Geometric Brownian Motion; Brownian Bridge