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Author: Graham Elliott
Publisher:
ISBN:
Category : Autoregression (Statistics)
Languages : en
Pages : 36
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Book Description
This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.
Author: Graham Elliott
Publisher:
ISBN:
Category : Autoregression (Statistics)
Languages : en
Pages : 36
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Book Description
This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.
Author:
Publisher:
ISBN:
Category : Power envelope
Languages : en
Pages :
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Author: David Bowman
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 66
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Book Description
Author: David Bowman
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this paper the class of admissable tests for unit roots in panel data sets of autoregressive, Gaussian time series will be partially characterized. Using this characterization, several recently suggested tests are shown to be inadmissable. Since the sufficient statistic for this testing problem is multidimensional, there is no uniformly most powerful test, however, in light of the inadmissability result, a new test is proposed that appears to do well relative to existing tests. The test is parameterized in a way that allows the choice of different directional deviations from the null hypothesis over which power is to be maximized, giving added flexibility to researchers.
Author: Joakim Westerlund
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
When testing for a unit root in a time series, in spite of the well-known power problem of univariate tests, it is quite common to use only the information regarding the autoregressive behaviour contained in that series. In a series of influential papers, Elliott et al. (Efficient tests for an autoregressive unit root, Econometrica 64, 813-836, 1996), Hansen (Rethinking the univariate approach to unit root testing: using covariates to increase power, Econometric Theory 11, 1148-1171, 1995a) and Seo (Distribution theory for unit root tests with conditional heteroskedasticity, Journal of Econometrics 91, 113-144, 1999) showed that this practice can be rather costly and that the inclusion of the extraneous information contained in the near-integratedness of many economic variables, their heteroskedasticity and their correlation with other covariates can lead to substantial power gains. In this article, we show how these information sets can be combined into a single unit root test.
Author: David Bowman
Publisher:
ISBN:
Category :
Languages : en
Pages : 56
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Book Description
Author: Badi H. Baltagi
Publisher: Elsevier
ISBN: 0762306882
Category : Business & Economics
Languages : en
Pages : 351
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Book Description
In the 16th Edition of Advances in Econometrics we present twelve papers discussing the current interface between Marketing and Econometrics. The authors are leading scholars in the fields and introduce the latest models for analysing marketing data. The papers are representative of the types of problems and methods that are used within the field of marketing. Marketing focuses on the interaction between the firm and the consumer. Economics encompasses this interaction as well as many others. Economics, along with psychology and sociology, provides a theoretical foundation for marketing.
Author: Eric Zivot
Publisher: Springer Science & Business Media
ISBN: 0387217630
Category : Business & Economics
Languages : en
Pages : 632
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Book Description
The field of financial econometrics has exploded over the last decade This book represents an integration of theory, methods, and examples using the S-PLUS statistical modeling language and the S+FinMetrics module to facilitate the practice of financial econometrics. This is the first book to show the power of S-PLUS for the analysis of time series data. It is written for researchers and practitioners in the finance industry, academic researchers in economics and finance, and advanced MBA and graduate students in economics and finance. Readers are assumed to have a basic knowledge of S-PLUS and a solid grounding in basic statistics and time series concepts. This Second Edition is updated to cover S+FinMetrics 2.0 and includes new chapters on copulas, nonlinear regime switching models, continuous-time financial models, generalized method of moments, semi-nonparametric conditional density models, and the efficient method of moments. Eric Zivot is an associate professor and Gary Waterman Distinguished Scholar in the Economics Department, and adjunct associate professor of finance in the Business School at the University of Washington. He regularly teaches courses on econometric theory, financial econometrics and time series econometrics, and is the recipient of the Henry T. Buechel Award for Outstanding Teaching. He is an associate editor of Studies in Nonlinear Dynamics and Econometrics. He has published papers in the leading econometrics journals, including Econometrica, Econometric Theory, the Journal of Business and Economic Statistics, Journal of Econometrics, and the Review of Economics and Statistics. Jiahui Wang is an employee of Ronin Capital LLC. He received a Ph.D. in Economics from the University of Washington in 1997. He has published in leading econometrics journals such as Econometrica and Journal of Business and Economic Statistics, and is the Principal Investigator of National Science Foundation SBIR grants. In 2002 Dr. Wang was selected as one of the "2000 Outstanding Scholars of the 21st Century" by International Biographical Centre.
Author: G. S. Maddala
Publisher: Cambridge University Press
ISBN: 9780521587822
Category : Business & Economics
Languages : en
Pages : 528
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Book Description
A comprehensive review of unit roots, cointegration and structural change from a best-selling author.
Author: Morten Ørregaard Nielsen
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung's (2002) test as the special case d = 1. It is shown that (i) each member of the family with d gt; 0 is consistent, (ii) the asymptotic distribution depends on d, and thus reflects the parameter chosen to implement the test, and (iii) since the asymptotic distribution depends on d and the test remains consistent for all d gt; 0, it is possible to analyze the power of the test for different values of d. The usual Phillips-Perron or Dickey-Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties. It is shown that members of the family with d lt; 1 have higher asymptotic local power than the Breitung (2002) test, and when d is small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear timetrend. Furthermore, GLS detrending is shown to improve power when d is small, which is not the case for Breitung's (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite sample power that is higher than that of Breitung's (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey-Fuller test with lag length chosen by an information criterion.
