Popularity of Unit Root Tests: A Review

Deviations of asset prices from the random walk dynamic imply the predictability of asset returns and thus have important implications for portfolio construction and risk management. This paper proposes a real-time monitoring device for such deviations using intraday high-frequency data. The proposed procedures are based on unit root tests with in-fill asymptotics but extended to take the empirical features of high-frequency financial data (particularly jumps) into consideration. We derive the limiting distributions of the tests under both the null hypothesis of a random walk with jumps and the alternative of mean reversion/explosiveness with jumps. The limiting results show that ignoring the presence of jumps could potentially lead to severe size distortions of both the standard left-sided (against mean reversion) and right-sided (against explosiveness) unit root tests. The simulation results reveal satisfactory performance of the proposed tests even with data from a relatively short time span. As an illustration, we apply the procedure to the Nasdaq composite index at the 10-minute frequency over two periods: around the peak of the dot-com bubble and during the 2015–2106 stock market sell-off. We find strong evidence of explosiveness in asset prices in late 1999 and mean reversion in late 2015. We also show that accounting for jumps when testing the random walk hypothesis on intraday data is empirically relevant and that ignoring jumps can lead to different conclusions.

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ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

Econometric Theory ◽

10.1017/s0266466614000656 ◽

2014 ◽

Vol 31 (3) ◽

pp. 539-559 ◽

Cited By ~ 5

Author(s):

I. Gaia Becheri ◽

Feike C. Drost ◽

Ramon van den Akker

Keyword(s):

Unit Root ◽

Generalized Least Squares ◽

Applied Economics ◽

Unit Root Tests ◽

Finite Sample ◽

Asymptotic Power ◽

Optimal Tests ◽

Independent Panel ◽

Local Asymptotic Power ◽

Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

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