A New Criterion for Lag-Length Selection in Unit Root Tests

Agunloye; Oluokun Kasali; Arnab; Raghunath; Shangodoyin; Dahud Kehinde

doi:doi:10.11648/j.ajtas.20130206.28

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A New Criterion for Lag-Length Selection in Unit Root Tests

Agunloye, Oluokun Kasali, Arnab, Raghunath, Shangodoyin, Dahud Kehinde

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)

Published: 30 January 2014

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Abstract

This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)
DOI	10.11648/j.ajtas.20130206.28
Page(s)	293-298
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Truncation Lag, Information Criteria, Koyck Distributed Lag Model, Unit Root Test, Low Power, Partial Correlation Coefficient

References

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[2]	Campbell, J. C. and Perron, P. (1991) "Pitfall and Opportunities: What Macroeconomists shouldknow about Unit Roots," NBER Technical Working Paper # 100
[3]	Xiao, Z. and Phillips, P. C. B. (1997) "An ADF Coefficient Test for a Unit Root in ARMAModels of Unknown Order with Empirical Applications to the U.S. Economy," CowlesFoundation Discussion Paper # 1161,
[4]	Maddala, G. S. and Kim, I. M. (1998) Unit Roots, Cointegration and Time Series, Cambridge University Press
[5]	Cavaliere, G. (2012) "Lag-length Selection for a Unit Root test in the presence of non-stationaryVolatility," Cowles Foundation Discussion Paper # 1844.
[6]	Dufour, J. M and King, M. L. (1991) "Optimal Invariant Tests for the Autocorrelation Coefficient in Linear Regressions with Stationary or Non-stationary AR(1) errors," Journal of Econometrics,47, 115-143
[7]	Said, E. S. and Dickey, D. A. (1984) "Testing for a Unit Root in Autoregressive Moving Average Models of Unknown Order," Biometrika, 71, 3, 599-607.
[8]	Elliott, G. Rothenberg, T. J. and Stock, J. H. (1996) "Efficient Tests for an Autoregressive UnitRoot," Econometrica, 64, 4, 813-836
[9]	Hall, A. (1994) "Testing for a Unit Root in Time Series with Pretest Data-based ModelSelection," Journal of Business and Economic Statistics, 12, 4, 461-470
[10]	Ng, S. and Perron, P. (2001) "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, 69, 6, 1519-1554
[11]	Shaowen Wu (2010)"Lag Length Selection In DF-GLS Unit Root Tests",Communication in Statistics-Simulation and computation,39:8,1590-1604
[12]	Akaike, H., 1969. Fitting Autoregressive Models for Prediction. Annalsof The Institute of Statistical Mathematics, 21(2), 243–247.
[13]	Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F., 2ndInternational Symposium on Information Theory. AkademiaiKiado`, Budapest, pp. 267–281.
[14]	Schwarz, G. (1978) " Estimating the dimension of a model". Annals of Statistics, 6, 461 –464.
[15]	Hannan, E. J. and Quinn, B. G. (1978). "The determination of the order of an autoregression". Journal of Royal Statistical Society, 41, 190 – 195.
[16]	Koyck, L.M. (1954), Distributed Lags and Investment Analysis, Amsterdam: North-Holland.
[17]	Gujarati, D.(2005),Essentials of Econometrics, McGraw-Hill School Education Group.

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APA Style

Agunloye, Oluokun Kasali, Arnab, Raghunath, Shangodoyin, et al. (2014). A New Criterion for Lag-Length Selection in Unit Root Tests. American Journal of Theoretical and Applied Statistics, 2(6), 293-298. https://doi.org/10.11648/j.ajtas.20130206.28

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ACS Style

Agunloye; Oluokun Kasali; Arnab; Raghunath; Shangodoyin, et al. A New Criterion for Lag-Length Selection in Unit Root Tests. Am. J. Theor. Appl. Stat. 2014, 2(6), 293-298. doi: 10.11648/j.ajtas.20130206.28

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AMA Style

Agunloye, Oluokun Kasali, Arnab, Raghunath, Shangodoyin, et al. A New Criterion for Lag-Length Selection in Unit Root Tests. Am J Theor Appl Stat. 2014;2(6):293-298. doi: 10.11648/j.ajtas.20130206.28

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@article{10.11648/j.ajtas.20130206.28,
  author = {Agunloye and Oluokun Kasali and Arnab and Raghunath and Shangodoyin and Dahud Kehinde},
  title = {A New Criterion for Lag-Length Selection in Unit Root Tests},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {6},
  pages = {293-298},
  doi = {10.11648/j.ajtas.20130206.28},
  url = {https://doi.org/10.11648/j.ajtas.20130206.28},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.28},
  abstract = {This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.},
 year = {2014}
}

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TY  - JOUR
T1  - A New Criterion for Lag-Length Selection in Unit Root Tests
AU  - Agunloye
AU  - Oluokun Kasali
AU  - Arnab
AU  - Raghunath
AU  - Shangodoyin
AU  - Dahud Kehinde
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.28
DO  - 10.11648/j.ajtas.20130206.28
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 293
EP  - 298
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.28
AB  - This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.
VL  - 2
IS  - 6
ER  -

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Author Information

Agunloye
Oluokun Kasali
Arnab
Raghunath
Shangodoyin
Dahud Kehinde

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APA Style

Agunloye, Oluokun Kasali, Arnab, Raghunath, Shangodoyin, et al. (2014). A New Criterion for Lag-Length Selection in Unit Root Tests. American Journal of Theoretical and Applied Statistics, 2(6), 293-298. https://doi.org/10.11648/j.ajtas.20130206.28

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ACS Style

Agunloye; Oluokun Kasali; Arnab; Raghunath; Shangodoyin, et al. A New Criterion for Lag-Length Selection in Unit Root Tests. Am. J. Theor. Appl. Stat. 2014, 2(6), 293-298. doi: 10.11648/j.ajtas.20130206.28

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AMA Style

Agunloye, Oluokun Kasali, Arnab, Raghunath, Shangodoyin, et al. A New Criterion for Lag-Length Selection in Unit Root Tests. Am J Theor Appl Stat. 2014;2(6):293-298. doi: 10.11648/j.ajtas.20130206.28

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@article{10.11648/j.ajtas.20130206.28,
  author = {Agunloye and Oluokun Kasali and Arnab and Raghunath and Shangodoyin and Dahud Kehinde},
  title = {A New Criterion for Lag-Length Selection in Unit Root Tests},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {6},
  pages = {293-298},
  doi = {10.11648/j.ajtas.20130206.28},
  url = {https://doi.org/10.11648/j.ajtas.20130206.28},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.28},
  abstract = {This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - A New Criterion for Lag-Length Selection in Unit Root Tests
AU  - Agunloye
AU  - Oluokun Kasali
AU  - Arnab
AU  - Raghunath
AU  - Shangodoyin
AU  - Dahud Kehinde
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.28
DO  - 10.11648/j.ajtas.20130206.28
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 293
EP  - 298
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.28
AB  - This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.
VL  - 2
IS  - 6
ER  -

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