Abstract
We review some recent results on goodness of fit test for the drift coefficient of a one-dimensional ergodic diffusion, where the diffusion coefficient is a nuisance function which however is estimated. Using a theory for the continuous observation case, we first present a test based on deterministic discrete time observations of the process. Then we also propose a test based on the data observed discretely in space, that is, the so-called tick time sample scheme. In both sampling schemes the limit distribution of the test is the supremum of the standard Brownian motion, thus the test is asymptotically distribution free. The tests are also consistent under any fixed alternatives.
| Original language | English |
|---|---|
| Pages (from-to) | 91-106 |
| Number of pages | 16 |
| Journal | Economic Notes |
| Volume | 39 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 2010 Feb |
| Externally published | Yes |
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Keywords
- C01
- C12
ASJC Scopus subject areas
- Economics and Econometrics
Cite this
Review on Goodness of Fit Tests for Ergodic Diffusion Processes by Different Sampling Schemes. / Negri, Ilia; Nishiyama, Yoichi.
In: Economic Notes, Vol. 39, No. 1-2, 02.2010, p. 91-106.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Review on Goodness of Fit Tests for Ergodic Diffusion Processes by Different Sampling Schemes
AU - Negri, Ilia
AU - Nishiyama, Yoichi
PY - 2010/2
Y1 - 2010/2
N2 - We review some recent results on goodness of fit test for the drift coefficient of a one-dimensional ergodic diffusion, where the diffusion coefficient is a nuisance function which however is estimated. Using a theory for the continuous observation case, we first present a test based on deterministic discrete time observations of the process. Then we also propose a test based on the data observed discretely in space, that is, the so-called tick time sample scheme. In both sampling schemes the limit distribution of the test is the supremum of the standard Brownian motion, thus the test is asymptotically distribution free. The tests are also consistent under any fixed alternatives.
AB - We review some recent results on goodness of fit test for the drift coefficient of a one-dimensional ergodic diffusion, where the diffusion coefficient is a nuisance function which however is estimated. Using a theory for the continuous observation case, we first present a test based on deterministic discrete time observations of the process. Then we also propose a test based on the data observed discretely in space, that is, the so-called tick time sample scheme. In both sampling schemes the limit distribution of the test is the supremum of the standard Brownian motion, thus the test is asymptotically distribution free. The tests are also consistent under any fixed alternatives.
KW - C01
KW - C12
UR - http://www.scopus.com/inward/record.url?scp=78049441642&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78049441642&partnerID=8YFLogxK
U2 - 10.1111/j.1468-0300.2010.00221.x
DO - 10.1111/j.1468-0300.2010.00221.x
M3 - Article
AN - SCOPUS:78049441642
VL - 39
SP - 91
EP - 106
JO - Economic Notes
JF - Economic Notes
SN - 0391-5026
IS - 1-2
ER -