focus on: james durbin august 2012
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Selected Readings –August 2012 1
SELECTED READINGS
Focus on: James Durbin
August 2012
Selected Readings –August 2012 2
INDEX
INTRODUCTION............................................................................................................. 6
1 WORKING PAPERS ............................................................................................... 7
1.1 Bernard Bercu and Frederic Proia, 2011. “A sharp analysis on the asymptotic behaviour
of the Durbin-Watson statistic for the first-order autoregressive process”. arXiv.org,
Quantitative Finance Papers No. 1104.3328. ........................................................................................ 7
1.2 Dimitris Hatzinikolaou, 2010. “Econometric Errors in an Applied Economics Article”.
Econ Journal, Econ Journal Watch, Volume 7 (2010), Issue 2 (May), Pages 107-112. .................... 7
1.3 Kleiber Christian and Krämer Walter, 2004. “Finite sample of the Durbin-Watson test
against fractionally integrated disturbances”. Technische Universität Dortmund,
Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen,
Technical Reports No. 2004, 15. ............................................................................................................ 8
1.4 Anatolyev Stanislav, 2003. “Durbin Watson Statistic and Random Individual Effects”.
Cambridge University Press, Econometric Theory. Volume 19 (2003), Issue 05 (October), Pages
882-883. 8
1.5 Jan Víšek, 2001. “Durbin-Watson Statistic for the Least Trimmed Squares”. The Czech
Econometric Society in its journal Bulletin of the Czech Econometric Society, Volume 8 (2001),
Issue 14. ................................................................................................................................................... 8
1.6 Nakamura Shisei and Taniguchi Masanobu, 1999. “Asymptotic Theory for the Durbin
Watson Statistic under Long-Memory Dependence”. Cambridge University Press in its journal
Econometric Theory, Volume 15 (1999), Issue 06 (December), Pages 847-866. ................................ 9
1.7 W. Tsay, 1998. “On the power of durbin-watson statistic against fractionally integrated
processes”. Taylor and Francis Journals in its journal Econometric Reviews. Volume 17 (1998),
Issue 4, Pages 361-386. ........................................................................................................................... 9
1.8 Watson G. S. ,1995. “Detecting a change in the intercept in multiple regressions”.
Elsevier, Statistics and Probability Letters, Volume 23 (1995), Issue 1 (April),Pages 69-72. ........ 10
1.9 Hisamatsu Hiroyuki and Maekawa Koichi,1994. “The distribution of the Durbin-Watson
statistic in integrated and near-integrated models”. Elsevier in its journal of Econometrics,
Volume 61 (1994),Issue 2 (April),Pages 367-382. ............................................................................... 10
1.10 Ghazal G. A. ,1994. “Moments of the ratio of two dependent quadratic forms”. Elsevier
in its journal Statistics and Probability Letters, Volume 20 (1994), Issue 4 (July), Pages 313-319.
11
1.11 Ali Mukhtar M. and Sharma Subhash C.,1993. “Robustness to nonnormality of the
Durbin-Watson test for autocorrelation”. Elsevier in its journal of Econometrics, Volume 57
(1993), Issue 1-3, Pages 117-136. ......................................................................................................... 11
1.12 Bartels Robert,1992. “On the power function of the Durbin-Watson test”. Elsevier in its
journal of Econometrics, Volume 51 (1992), Issue 1-2, Pages 101-112. ........................................... 11
1.13 White Kenneth J. ,1992. “The Durbin-Watson Test for Autocorrelation in Nonlinear
Models”. MIT Press in its journal Review of Economics and Statistics, Volume 74 (1992), Issue 2
(May), Pages 370-73.............................................................................................................................. 12
Selected Readings –August 2012 3
1.14 Ansley Craig F. , Kohn Robert and Shively Thomas S.,1992. “Computing p-values for
the generalized Durbin-Watson and other invariant test statistics”. Elsevier in its journal of
Econometrics, Volume 54 (1992),Issue 1-3 ,Pages 277-300. .............................................................. 12
1.15 Grose Simone D. and King Maxwell L., 1991. “The locally unbiased two-sided Durbin--
Watson test”. Elsevier in its journal Economics Letters, Volume 35 (1991), Issue 4 (April), Pages
401-407. 13
1.16 Giles David E. A. and Small John P., 1991. “The power of the Durbin-Watson test when
the errors are heteroscedastic”. Elsevier in its journal Economics Letters, Volume 36 (1991),
Issue 1 (May),Pages 37-41. ................................................................................................................... 13
1.17 Sneek J.M., 1991. “On the approximation of the Durbin-Watson statistic in O(n)
operations”. VU University Amsterdam, Faculty of Economics, Business Administration and
Econometrics in its series Serie Research Memoranda No. 0021. .................................................... 13
1.18 King Maxwell L. and Wu Ping X., 1991. “Small-disturbance asymptotic and the Durbin-
Watson and related tests in the dynamic regression model”. Elsevier in its journal of
Econometrics, Volume 47 (1991), Issue 1 (January), Pages 145-152. ............................................... 14
1.19 Phillips Peter C. B. and Loretan Mico, 1991. “The Durbin-Watson ratio under infinite-
variance errors”. Elsevier in its journal of Econometrics, Volume (Year): 47 (1991), Issue 1
(January), Pages 85-114. ...................................................................................................................... 14
1.20 Kariya Takeaki, 1988. “The Class of Models for which the Durbin-Watson Test is locally
optimal”. Department of Economics, University of Pennsylvania and Osaka University Institute
of Social and Economic Research Association in its journal International Economic Review,
Volume 29 (1988), Issue 1 (February), Pages 167-75. ........................................................................ 15
1.21 King Maxwell L. and Evans Merran A., 1988. “Locally Optimal Properties of the
Durbin-Watson Test”. Cambridge University Press in its journal Econometric Theory, Volume 4
(1988), Issue 03 (December), Pages 509-516. ...................................................................................... 15
1.22 Durbin James, 1988. “Maximum Likelihood Estimation of the Parameters of a System of
Simultaneous Regression Equations”. Cambridge University Press, Econometric Theory, Volume
4 (1988), Issue 01 (April), Pages 159-170. ........................................................................................... 15
1.23 Srivastava M. S., 1987. “Asymptotic distribution of Durbin-Watson statistic”. Elsevier in
its journal Economics Letters, Volume 24 (1987), Issue 2, Pages 157-160. ...................................... 16
1.24 Inder Brett, 1986. “An Approximation to the Null Distribution of the Durbin-Watson
Statistic in Models Containing Lagged Dependent Variables”. Cambridge University Press in its
journal Econometric Theory, Volume 2 (1986), Issue 03 (December), Pages 413-428. .................. 16
1.25 Jeong Ki-Jun, 1985. “A New Approximation of the Critical Point of the Durbin-Watson
Test for Serial Correlation”. Econometric Society in its journal Econometrica, Volume 53 (1985),
Issue 2 (March), Pages 477-82. ............................................................................................................ 17
1.26 King Maxwell L. and Evans Merran A., 1985. “The Durbin-Watson test and cross-
sectional data”. Elsevier in its journal Economics Letters, Volume 18 (1985), Issue 1, Pages 31-34.
17
1.27 Dufour Jean-Marie and Dagenais Marcel G., 1985. “Durbin-Watson tests for serial
correlation in regressions with missing observations”. ..................................................................... 17
1.28 Kramer W., 1985. “The power of the Durbin-Watson test for regressions without an
intercept”. Elsevier in its journal of Econometrics, Volume 28 (1985), Issue 3 (June), Pages 363-
370. 18
Selected Readings –August 2012 4
1.29 King Maxwell L., 1983. “The Durbin-Watson test for serial correlation: Bounds for
regressions using monthly data”. Elsevier in its journal of Econometrics, Volume 21 (1983), Issue
3 (April), Pages 357-366. ...................................................................................................................... 18
1.30 Bartels Robert and Goodhew John, 1981. “The Robustness of the Durbin-Watson Test”.
MIT Press in its journal Review of Economics and Statistics, Volume 63 (1981), Issue 1
(February), Pages 136-39. .................................................................................................................... 18
1.31 King M. L., 1981. “The alternative Durbin-Watson test: An assessment of Durbin and
Watson's choice of test statistic”. Elsevier in its journal of Econometrics, Volume 17 (1981), Issue
1 (September), Pages 51-66. ................................................................................................................. 18
1.32 King Maxwell L., 1981. “The Durbin-Watson Test for Serial Correlation: Bounds for
Regressions with Trend and/or Seasonal Dummy Variables”. Econometric Society in its journal
Econometrica, Volume 49 (1981), Issue 6 (November), Pages 1571-81. ........................................... 19
1.33 Farebrother R. W., 1980. “The Durbin-Watson Test for Serial Correlation When There
Is No Intercept in the Regression”. Econometric Society in its journal Econometrica, Volume 48
(1980), Issue 6 (September), Pages 1553-63. ....................................................................................... 19
1.34 Fomby Thomas B. and Guilkey David K., 1978. “On choosing the optimal level of
significance for the Durbin-Watson test and the Bayesian alternative”. Elsevier in its journal of
Econometrics, Volume 8 (1978), Issue 2 (October), Pages 203-213. ................................................. 19
1.35 Savin N. Eugene and White Kenneth J., 1977. “The Durbin-Watson Test for Serial
Correlation with Extreme Sample Sizes or Many Regressors”. Econometric Society in its journal
Econometrica, Volume 45 (1977), Issue 8 (November), Pages 1989-96. ........................................... 20
1.36 L' Esperance Wilford L., Chall Daniel and Taylor Daniel, 1976. “An Algorithm for
Determining the Distribution Function of the Durbin-Watson Test Statistic”. Econometric
Society in its journal Econometrica, Volume 44 (1976), Issue 6 (November), Pages 1325-26. ....... 20
1.37 Harrison M. J., 1975. “The Power of the Durbin-Watson and Geary Tests: Comment
and Further Evidence”. MIT Press in its journal Review of Economics and Statistics, Volume 57
(1975), Issue 3 (August), Pages 377-79. ............................................................................................... 20
1.38 Schmidt Peter and Guilkey David K., 1975. “Some Further Evidence on the Power of the
Durbin-Watson and Geary Tests”. MIT Press in its journal Review of Economics and Statistics,
Volume 57 (1975), Issue 3 (August), Pages 379-82. ............................................................................ 20
1.39 Tillman John A., 1975. “The Power of the Durbin-Watson Test”. Econometric Society in
its journal Econometrica, Volume 43 (1975), Issue 5-6 (Sept.-Nov.), Pages 959-74. ....................... 20
1.40 Blattberg Robert C. ,1973. “Evaluation of the Power of the Durbin-Watson Statistic for
Non-First Order Serial Correlation Alternatives”. MIT Press in its journal Review of Economics
and Statistics, Volume 55 (1973), Issue 4 (November), Pages 508-15. .............................................. 21
1.41 Habibagahi Hamid and Pratschke John L., 1972. “A Comparison of the Power of the
von Neumann Ratio, Durbin-Watson and Geary Tests”. MIT Press in its journal Review of
Economics and Statistics, Volume 54 (1972), Issue 2 (May), Pages179-85. ..................................... 21
2 SOFTWARE MODULE ......................................................................................... 22
2.1 Christopher F. Baum and Vince Wiggins, 1999. “DURBINH: Stata module to calculate
Durbin's h test for serial correlation”. Boston College Department of Economics in its series
Statistical Software Components No. S387301................................................................................... 22
Selected Readings –August 2012 5
2.2 Ludwig Kanzler, 1998. “DWATSON: MATLAB module to calculate Durbin-Watson
statistic and significance”. Software component provided by Boston College Department of
Economics in its series Statistical Software Components No. T850802. .......................................... 22
3 BOOK....................................................................................................................... 23
3.1 Durbin James and Koopman Siem Jan, 2012. “Time Series Analysis by State Space
Methods: Second Edition”. .................................................................................................................. 23
4 INTERVIEW ........................................................................................................... 24
4.1 Phillips Peter C. B., 1988. “The ET Interview: Professor James Durbin”. Cambridge
University Press, Econometric Theory, Volume 4 (1988), Issue 01 (April), Pages 125-157. .......... 24
Selected Readings –August 2012 6
INTRODUCTION
Professor James Durbin passed away on 23 June 2012 in London, at the age of 88.
James Durbin was born in 1923, in Wigan, England. He was educated at St John’s
College, Cambridge. He was Professor of Statistics at the LSE until his retirement in
1988, during which time he was a Council member and vice president of the Royal
Statistical Society for a number of years before becoming President (1986-87). As
well as his tenure ship as RSS President, he was a Fellow of the British Academy and
President of the International Statistical Institute. In 2008 he was awarded the Guy
Medal in Gold for a lifetime’s achievement in statistics.
James Durbin’s research has made very significant contributions to the fields of
statistics and econometrics. Together with Australian researcher Geof Watson, he
developed the well known Durbin-Watson test statistic for serial correlation in
regression residuals. His work on errors in variables led to the development of the
Durbin-Wu-Hausman test, and he was also responsible for the Durbin-Levinson
method, which is implemented in most time series software packages.
Although much of his work was theory based, he also tackled practical issues, such as
the effects of seat belt legislation on road casualties in Great Britain, a project that led
him to develop methods for estimating time series with non-Gaussian features.
What follows is a non-exhaustive collection of materials related on James Durbin’s
work.
Contact point: GianLuigi Mazzi, "Responsible for Euro-indicators and statistical
methodology", Estat – C4 "Key Indicators for European Policies"
gianluigi.mazzi@ec.europa.eu.
Selected Readings –August 2012 7
1 WORKING PAPERS
1.1 Bernard Bercu and Frederic Proia, 2011. “A sharp analysis on the
asymptotic behaviour of the Durbin-Watson statistic for the first-
order autoregressive process”. arXiv.org, Quantitative Finance
Papers No. 1104.3328.
The purpose of this paper is to provide a sharp analysis on the asymptotic behaviour
of the Durbin-Watson statistic. We focus our attention on the first-order
autoregressive process where the driven noise is also given by a first-order
autoregressive process. We establish the almost sure convergence and the asymptotic
normality for both the least squares estimator of the unknown parameter of the
autoregressive process as well as for the serial correlation estimator associated to the
driven noise. In addition, the almost sure rates of convergence of our estimates are
also provided. It allows us to establish the almost sure convergence and the
asymptotic normality for the Durbin-Watson statistic. Finally, we propose a new
bilateral statistical test for residual autocorrelation.
Full text available at:
http://arxiv.org/abs/1104.3328
1.2 Dimitris Hatzinikolaou, 2010. “Econometric Errors in an Applied
Economics Article”. Econ Journal, Econ Journal Watch, Volume 7
(2010), Issue 2 (May), Pages 107-112.
This comment points out some econometric errors contained in an Applied
Economics article by Mavrommati and Papadopoulos (2005), to wit, the authors make
an incorrect statement about the standard F-test; they claim erroneously that the
Durbin-Watson test is irrelevant in panel data; they fail to test for serial correlation
and random-walk errors; and they misuse the Durbin-Wu-Hausman test for the
consistency of the fixed-effects estimator. Thus, their results are questionable. This
comment aims to prevent novice researchers from repeating these errors, and to police
standards at the journals.
Full text available at:
http://econjwatch.org/file_download/434/HatzinikolauMay2010.pdf
Selected Readings –August 2012 8
1.3 Kleiber Christian and Krämer Walter, 2004. “Finite sample of the
Durbin-Watson test against fractionally integrated disturbances”.
Technische Universität Dortmund, Sonderforschungsbereich 475:
Komplexitätsreduktion in multivariaten Datenstrukturen, Technical
Reports No. 2004, 15.
We consider the finite sample power of various tests against serial correlation in the
disturbances of a linear regression when these disturbances follow a stationary long
memory process. It emerges that the power depends on the form of the regressor
matrix and that, for the Durbin-Watson test and many other tests that can be written as
ratios of quadratic forms in the disturbances, the power can drop to zero for certain
regressors. We also provide a means to detect this zero-power trap. Our results
depend solely on the correlation structure and allow for fairly arbitrary nonlinearities
Full text available at:
http://econstor.eu/bitstream/10419/49321/1/384011888.pdf
1.4 Anatolyev Stanislav, 2003. “Durbin Watson Statistic and Random
Individual Effects”. Cambridge University Press, Econometric
Theory. Volume 19 (2003), Issue 05 (October), Pages 882-883.
No abstract is available.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=261002
1.5 Jan Víšek, 2001. “Durbin-Watson Statistic for the Least Trimmed
Squares”. The Czech Econometric Society in its journal Bulletin of
the Czech Econometric Society, Volume 8 (2001), Issue 14.
The famous Durbin-Watson statistic is studied for the residuals from the least
trimmed squared regression analysis. Having proved asymptotic linearity of
corresponding functional (namely sum of h smallest squared residuals), an asymptotic
representation of the least trimmed squares estimator is established. It is then used to
modify D-W considerations which led to the analytically tractable form of D-W
statistic. It appeared that in the modified D-W statistic for the least trimmed squares
the terms which are different from the terms appearing in D-W statistic for the
ordinary least squares, contain only a finite number of summands. Since all these
terms are uniformly with respect to the number of observations bounded in
probability, it is clear that asymptotically both versions, the first one for the ordinary
least squares and the second for the least trimmed squares, are equivalent.
Selected Readings –August 2012 9
Nevertheless some rough analysis of behaviour for finite samples is included at the
end of paper.
Full text available at:
http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/100
1.6 Nakamura Shisei and Taniguchi Masanobu, 1999. “Asymptotic
Theory for the Durbin Watson Statistic under Long-Memory
Dependence”. Cambridge University Press in its journal Econometric
Theory, Volume 15 (1999), Issue 06 (December), Pages 847-866.
In time series regression models with short-memory residual processes, the Durbin
Watson statistic (DW) has been used for the problem of testing for independence of
the residuals. In this paper we elucidate the asymptotic of DW for long-memory
residual processes. A standardized Durbin Watson statistic (SDW) is proposed. Then
we derive the asymptotic distributions of SDW under both the null and local
alternative hypotheses. Based on this result we evaluate the local power of SDW.
Numerical studies for DW and SDW are given.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=35219
1.7 W. Tsay, 1998. “On the power of durbin-watson statistic against
fractionally integrated processes”. Taylor and Francis Journals in its
journal Econometric Reviews. Volume 17 (1998), Issue 4, Pages 361-
386.
This paper provides the theoretical explanation and Monte Carlo experiments of using
a modified version of Durbin-Watson ( D W ) statistic to test an 1 ( 1 ) process against
I ( d ) alternatives, that is, integrated process of order d, where d is a fractional
number. We provide the exact order of magnitude of the modified D W test when the
data generating process is an I ( d ) process with d E (0. 1.5). Moreover, the
consistency of the modified DW statistic as a unit root test against I ( d ) alternatives
with d E ( 0 , l ) U ( 1 , 1.5) is proved in this paper. In addition to the theoretical
analysis, Monte Carlo experiments show that the performance of the modified D W
statistic reveals that it can be used as a unit root test against I ( d ) alternatives.
Access to full text is restricted to subscribers:
http://www.tandfonline.com/doi/abs/10.1080/07474939808800423
Selected Readings –August 2012 10
1.8 Watson G. S. ,1995. “Detecting a change in the intercept in multiple
regressions”. Elsevier, Statistics and Probability Letters, Volume 23
(1995), Issue 1 (April),Pages 69-72.
To detect a change at some unknown time in the constant term of a multiple
regression, an obvious statistic is the ratio c2 of the sum of squares of the partial sums
of the residuals to their sum of squares. We show how the methods of Durbin and
Watson (1950) can be used to find the true and an approximate significance point of
c2, and computable bounds for the true points.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/
1.9 Hisamatsu Hiroyuki and Maekawa Koichi,1994. “The distribution of
the Durbin-Watson statistic in integrated and near-integrated
models”. Elsevier in its journal of Econometrics, Volume 61
(1994),Issue 2 (April),Pages 367-382.
The Durbin-Watson (DW) statistics can be used in testing for a unit root in time series
regression. For this practical purpose, we calculate tabulated values of the critical
points for various sample size and levels of significance when the true model is a
first-order autoregression with a unit root and i.i.d. normal error. To calculate the
tables we obtain expressions for the exact and limiting cumulative distributions and
probability density functions of the DW statistic. Although the expressions obtained
in this paper are not closed form, tables can be obtained by numerical integration. For
comparisons of the power and asymptotic properties we also calculate the exact and
asymptotic cumulative distribution functions of the OLS estimator which can be used
as a test statistic for a unit root. Furthermore, power comparisons are made among
DW, OLS, and t statistics by simulation method. As a result it is shown that the DW
statistic can be used as an alternative test for detecting a unit root.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/0304407694900906
Selected Readings –August 2012 11
1.10 Ghazal G. A. ,1994. “Moments of the ratio of two dependent
quadratic forms”. Elsevier in its journal Statistics and Probability
Letters, Volume 20 (1994), Issue 4 (July), Pages 313-319.
Exact moments of the ratio of two dependent quadratic forms are derived in the case
when the variables involved are multivariate normal, and the quadratic form in the
denominator is idempotent. Application of the method to the Durbin--Watson statistic
is given.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/0167715294900191
1.11 Ali Mukhtar M. and Sharma Subhash C.,1993. “Robustness to
nonnormality of the Durbin-Watson test for autocorrelation”.
Elsevier in its journal of Econometrics, Volume 57 (1993), Issue 1-3,
Pages 117-136.
This study investigates the robustness to nonnormality of the null distribution of the
Durbin-Watson test for autocorrelation in regression errors. The first four moments of
the null distribution are derived to the order when the regression errors are
non normal, with n the sample size. It is found that nonnormality has an insignificant
effect on the mean and the fourth central moment of the distribution. The variance
tends to be deflated (inflated) if the error distribution is long-tailed (short-tailed). The
third central moment is reduced if the error distribution is skewed (left or right). Both
skewness and kurtosis of the distribution are affected by nonnormality, but these
effects are negligible in large samples. It seems the test is relatively robust for
moderate nonnormality and moderately large sample size. These effects are also
found to have insignificant influence from the regressors.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/0304407693900619
1.12 Bartels Robert,1992. “On the power function of the Durbin-Watson
test”. Elsevier in its journal of Econometrics, Volume 51 (1992), Issue
1-2, Pages 101-112.
Recent papers have drawn attention to the fact that the power function of the Durbin-
Watson (DW) test against the alternative of a stationary first-order autoregression, is
not necessarily monotonic as p departs from the null hypothesis that p = 0. Indeed for
some data sets the power tends to 0 as p →±1, making inferences based on the DW
Selected Readings –August 2012 12
test meaningless. The purpose of the present study is twofold. First, the paper
provides new insight into the factors underlying this worrisome aspect of the DW
power function and shows that it is not restricted to stationary processes. Second, the
paper presents a fairly easily calculated boundary power function which for any given
data set gives some guidance as to whether or not the DW test will have poor power
properties.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/030440769290031L
1.13 White Kenneth J. ,1992. “The Durbin-Watson Test for
Autocorrelation in Nonlinear Models”. MIT Press in its journal
Review of Economics and Statistics, Volume 74 (1992), Issue 2 (May),
Pages 370-73.
This paper shows a simple method for approximating the exact distribution of the
Durbin-Watson test statistic for first-order autocorrelation in a nonlinear model. The
proposed approximate nonlinear Durbin-Watson test has good size and power when
compared to alternatives.
Access to full text is restricted to subscribers:
http://www.jstor.org
1.14 Ansley Craig F. , Kohn Robert and Shively Thomas S.,1992.
“Computing p-values for the generalized Durbin-Watson and other
invariant test statistics”. Elsevier in its journal of Econometrics,
Volume 54 (1992),Issue 1-3 ,Pages 277-300.
Shively, Ansley, and Kohn (1990) give an O (n) algorithm for computing the p-values
of the Durbin-Watson and other invariant test statistics in time series regression. They
do so by evaluating the characteristic function of a quadratic form in standard normal
random variables and then numerically inverting it. In this paper we obtain a new
expression for the characteristic function which simplifies the handling of the
independent regressors and so is easier to evaluate. We also obtain general, easily
computable bounds on the integration and truncation errors which arise in the
numerical inversion of the characteristic function. Empirical results are presented on
the speed and accuracy of our algorithm.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/0304407692901095
Selected Readings –August 2012 13
1.15 Grose Simone D. and King Maxwell L., 1991. “The locally unbiased
two-sided Durbin--Watson test”. Elsevier in its journal Economics
Letters, Volume 35 (1991), Issue 4 (April), Pages 401-407.
An algorithm for constructing locally unbiased two-sided critical regions for the
Durbin–Watson test is presented. It can also be applied to other two-sided tests.
Empirical calculations suggest that, at least for the Durbin–Watson test, the current
practice of using equal-tailed critical values yields approximately locally unbiased
critical regions.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/016517659190010I
1.16 Giles David E. A. and Small John P., 1991. “The power of the Durbin-
Watson test when the errors are heteroscedastic”. Elsevier in its
journal Economics Letters, Volume 36 (1991), Issue 1 (May),Pages
37-41.
We consider the robustness of the Durbin-Watson test to mis-specification via
heteroscedastic disturbances. Exact powers are calculated using real and artificial
regressors. We find that heteroscedasticity may dramatically alter the power of the
test.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/016517659190052M
1.17 Sneek J.M., 1991. “On the approximation of the Durbin-Watson
statistic in O(n) operations”. VU University Amsterdam, Faculty of
Economics, Business Administration and Econometrics in its series
Serie Research Memoranda No. 0021.
No abstract is available.
Full text available at:
ftp://zappa.ubvu.vu.nl/19910021.pdf
Selected Readings –August 2012 14
1.18 King Maxwell L. and Wu Ping X., 1991. “Small-disturbance
asymptotic and the Durbin-Watson and related tests in the dynamic
regression model”. Elsevier in its journal of Econometrics, Volume 47
(1991), Issue 1 (January), Pages 145-152.
Until recently, it was thought inappropriate to apply the Durbin-Watson (DW) test to
a dynamic linear regression model because of the lack of appropriate critical values.
Recently, Inder (1986) used a modified small-disturbance distribution (SDD) to find
approximate critical values. This paper studies the exact SDD of statistics of the same
general form as the DW statistic and suggests some changes to Inder's result. We
show how to calculate true small-disturbance critical values and bounds for these
critical values that take into account the exogenous regressors. Our results give a
justification for the use of the familiar tables of bounds when the DW test is applied to
a dynamic regression model.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/030440769190081N
1.19 Phillips Peter C. B. and Loretan Mico, 1991. “The Durbin-Watson
ratio under infinite-variance errors”. Elsevier in its journal of
Econometrics, Volume (Year): 47 (1991), Issue 1 (January), Pages 85-
114.
This paper studies the properties of the von Neumann ratio for time series with
infinite variance. The asymptotic theory is developed using recent results on the weak
convergence of partial sums of time series with infinite variance to stable processes
and of sample serial correlations to functions of stable variables. Our asymptotic
cover the null of iid variates and general moving average (MA) alternatives.
Regression residuals are also considered. In the static regression model the Durbin-
Watson statistic has the same limit distribution as the von Neumann ratio under
general conditions. However, the dynamic models, the results are more complex and
more interesting. When the regressors have thicker tail probabilities than the errors we
find that the Durbin-Watson and von Neumann ration asymptotic are the same.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/030440769190079S
Selected Readings –August 2012 15
1.20 Kariya Takeaki, 1988. “The Class of Models for which the Durbin-
Watson Test is locally optimal”. Department of Economics,
University of Pennsylvania and Osaka University Institute of Social
and Economic Research Association in its journal International
Economic Review, Volume 29 (1988), Issue 1 (February), Pages 167-
75.
No abstract is available.
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1.21 King Maxwell L. and Evans Merran A., 1988. “Locally Optimal
Properties of the Durbin-Watson Test”. Cambridge University Press
in its journal Econometric Theory, Volume 4 (1988), Issue 03
(December), Pages 509-516.
Although originally designed to detect AR (1) disturbances in the linear-regression
model, the Durbin-Watson test is known to have good power against other forms of
disturbance behavior. In this paper, we identify disturbance processes involving any
number of parameters against which the Durbin–Watson test is approximately locally
best invariant uniformly in a range of directions from the null hypothesis. Examples
include the sum of q independent ARMA (1,1) processes, certain spatial
autocorrelation processes involving up to four parameters, and a stochastic cycle
model.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=790610
6
1.22 Durbin James, 1988. “Maximum Likelihood Estimation of the
Parameters of a System of Simultaneous Regression Equations”.
Cambridge University Press, Econometric Theory, Volume 4 (1988),
Issue 01 (April), Pages 159-170.
Procedures for computing the full information maximum likelihood (FIML) estimates
of the parameters of a system of simultaneous regression equations have been
described by Koopmans, Rubin, and Leipnik, Chernoff and Divinsky, Brown, and
Eisenpress. However, all of these methods are rather complicated since they are based
on estimating equations that are expressed in an inconvenient form. In this paper, a
transformation of the maximum likelihood (ML) equations is developed which not
only leads to simpler computations but which also simplifies the study of the
Selected Readings –August 2012 16
properties of the estimates. The equations are obtained in a form which is capable of
solution by a modified Newton-Raphson iterative procedure. The form obtained also
shows up very clearly the relation between the maximum likelihood estimates and
those obtained by the three-stage least squares method of Zellner and Theil.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=790591
2
1.23 Srivastava M. S., 1987. “Asymptotic distribution of Durbin-Watson
statistic”. Elsevier in its journal Economics Letters, Volume 24
(1987), Issue 2, Pages 157-160.
In this note the asymptotic distribution of Durbin–Watson statistic is established
without any condition on the design matrix.
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http://www.sciencedirect.com/science/article/pii/0165176587902436
1.24 Inder Brett, 1986. “An Approximation to the Null Distribution of the
Durbin-Watson Statistic in Models Containing Lagged Dependent
Variables”. Cambridge University Press in its journal Econometric
Theory, Volume 2 (1986), Issue 03 (December), Pages 413-428.
We consider testing for autoregressive disturbances in the linear regression model
with a lagged dependent variable. An approximation to the null distribution of the
Durbin—Watson statistic is developed using small-disturbance asymptotics, and is
used to obtain test critical values. We also obtain non similar critical values for the
Durbin-Watson and Durbin's h and t tests. Monte Carlo results are reported comparing
the performances of the tests under the null and alternative hypotheses. The Durbin-
Watson test is found to be more powerful and to perform more consistently than either
of Durbin's tests under Ho.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=790646
1
Selected Readings –August 2012 17
1.25 Jeong Ki-Jun, 1985. “A New Approximation of the Critical Point of
the Durbin-Watson Test for Serial Correlation”. Econometric Society
in its journal Econometrica, Volume 53 (1985), Issue 2 (March),
Pages 477-82.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
1.26 King Maxwell L. and Evans Merran A., 1985. “The Durbin-Watson
test and cross-sectional data”. Elsevier in its journal Economics
Letters, Volume 18 (1985), Issue 1, Pages 31-34.
This note presents some models of disturbance behaviour that may be useful in
regression models based on cross-sectional data with a degree of natural ordering. The
Durbin-Watson test is shown to approximately locally best invariant against these
models.
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1.27 Dufour Jean-Marie and Dagenais Marcel G., 1985. “Durbin-Watson
tests for serial correlation in regressions with missing observations”.
We study two Durbin-Watson type tests for serial correlation of errors in regression
models when observations are missing. We derive them by applying standard methods
used in time series and linear models to deal with missing observations. The first test
may be viewed as a regular Durbin-Watson test in the context of an extended model.
We discuss appropriate adjustments that allow one to use all available bounds tables.
We show that the test is locally most powerful invariant against the same alternative
error distribution as the Durbin-Watson test. The second test is based on a modified
Durbin-Watson statistic suggested by King (1981a) and is locally most powerful
invariant against a first-order autoregressive process.
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Selected Readings –August 2012 18
1.28 Kramer W., 1985. “The power of the Durbin-Watson test for
regressions without an intercept”. Elsevier in its journal of
Econometrics, Volume 28 (1985), Issue 3 (June), Pages 363-370.
In the linear regression model without an intercept, the limiting power of the Durbin–
Watson test (as correlation among errors increases) is shown to take only one of two
values. This is either one or zero, depending on the underlying regressor matrix. Some
examples and a simple rule to decide from a given regressor matrix which of these
cases applies are also given.
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1.29 King Maxwell L., 1983. “The Durbin-Watson test for serial
correlation: Bounds for regressions using monthly data”. Elsevier in
its journal of Econometrics, Volume 21 (1983), Issue 3 (April), Pages
357-366.
This paper extends existing tables of bounds on critical values of the Durbin-Watson
test for regressions with an intercept and regressions with an intercept plus a linear
trend. It also presents tables of bounds for regressions with a full set of monthly
seasonal dummy variables, both with and without a linear trend regressor.
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1.30 Bartels Robert and Goodhew John, 1981. “The Robustness of the
Durbin-Watson Test”. MIT Press in its journal Review of Economics
and Statistics, Volume 63 (1981), Issue 1 (February), Pages 136-39.
No abstract is available.
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1.31 King M. L., 1981. “The alternative Durbin-Watson test: An
assessment of Durbin and Watson's choice of test statistic”. Elsevier
in its journal of Econometrics, Volume 17 (1981), Issue 1
(September), Pages 51-66.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.sciencedirect.com/science/article/pii/0304407681900580
Selected Readings –August 2012 19
1.32 King Maxwell L., 1981. “The Durbin-Watson Test for Serial
Correlation: Bounds for Regressions with Trend and/or Seasonal
Dummy Variables”. Econometric Society in its journal Econometrica,
Volume 49 (1981), Issue 6 (November), Pages 1571-81.
This paper examines Durbin and Watson's (1950) choice of test statistic for their test
of first-order autoregressive regression disturbances. Attention is focused on an
alternative statistic, d'. Theoretical and empirical power properties of the d' test are
compared with those of the Durbin-Watson test. The former is found to be locally best
invariant while the latter is approximately locally best invariant. The d' test is also
found to be more powerful than its counterpart against negative autocorrelation and
for small values of the autocorrelation coefficient against positive autocorrelation.
Selected bounds for significance points of d' are tabulated.
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1.33 Farebrother R. W., 1980. “The Durbin-Watson Test for Serial
Correlation When There Is No Intercept in the Regression”.
Econometric Society in its journal Econometrica, Volume 48 (1980),
Issue 6 (September), Pages 1553-63.
No abstract is available.
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1.34 Fomby Thomas B. and Guilkey David K., 1978. “On choosing the
optimal level of significance for the Durbin-Watson test and the
Bayesian alternative”. Elsevier in its journal of Econometrics,
Volume 8 (1978), Issue 2 (October), Pages 203-213.
This paper critically evaluates the usual ad hoc selection of the level of significance in
the Durbin-Watson test and compares this procedure to the Bayesian alternative. The
results of Monte Carlo experiments indicate that a α-level substantially larger than
that normally used may be appropriate. The Bayesian estimator performed better than
all preliminary test estimates in terms of MSE.
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Selected Readings –August 2012 20
1.35 Savin N. Eugene and White Kenneth J., 1977. “The Durbin-Watson
Test for Serial Correlation with Extreme Sample Sizes or Many
Regressors”. Econometric Society in its journal Econometrica,
Volume 45 (1977), Issue 8 (November), Pages 1989-96.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
1.36 L' Esperance Wilford L., Chall Daniel and Taylor Daniel, 1976. “An
Algorithm for Determining the Distribution Function of the Durbin-
Watson Test Statistic”. Econometric Society in its journal
Econometrica, Volume 44 (1976), Issue 6 (November), Pages 1325-26.
No abstract is available.
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1.37 Harrison M. J., 1975. “The Power of the Durbin-Watson and Geary
Tests: Comment and Further Evidence”. MIT Press in its journal
Review of Economics and Statistics, Volume 57 (1975), Issue 3
(August), Pages 377-79.
No abstract is available.
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1.38 Schmidt Peter and Guilkey David K., 1975. “Some Further Evidence
on the Power of the Durbin-Watson and Geary Tests”. MIT Press in
its journal Review of Economics and Statistics, Volume 57 (1975),
Issue 3 (August), Pages 379-82.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
1.39 Tillman John A., 1975. “The Power of the Durbin-Watson Test”.
Econometric Society in its journal Econometrica, Volume 43 (1975),
Issue 5-6 (Sept.-Nov.), Pages 959-74.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
Selected Readings –August 2012 21
1.40 Blattberg Robert C. ,1973. “Evaluation of the Power of the Durbin-
Watson Statistic for Non-First Order Serial Correlation
Alternatives”. MIT Press in its journal Review of Economics and
Statistics, Volume 55 (1973), Issue 4 (November), Pages 508-15.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
1.41 Habibagahi Hamid and Pratschke John L., 1972. “A Comparison of
the Power of the von Neumann Ratio, Durbin-Watson and Geary
Tests”. MIT Press in its journal Review of Economics and Statistics,
Volume 54 (1972), Issue 2 (May), Pages179-85.
No abstract is available.
Access to full text is restricted to subscribers:
http://www.jstor.org
Selected Readings –August 2012 22
2 SOFTWARE MODULE
2.1 Christopher F. Baum and Vince Wiggins, 1999. “DURBINH: Stata
module to calculate Durbin's h test for serial correlation”. Boston
College Department of Economics in its series Statistical Software
Components No. S387301.
In the presence of lagged dependent variables, the Durbin-Watson statistic and Box-
Pierce Q statistics are not appropriate tests for serial correlation in the errors. Durbin's
h statistic may be used in this context. An asymptotically equivalent variant of
Durbin's h statistic is computed by this command. This is version 1.04 of the software,
updated from that published in STB-55. The force option has been added to allow
durbinh to be employed after regress, robust and newey. The test is built in to Stata 8
as "durbina"; also see "durbina2" which will work on a single time series of a panel.
Full module available at:
http://fmwww.bc.edu/repec/bocode/d/durbinh.ado
2.2 Ludwig Kanzler, 1998. “DWATSON: MATLAB module to calculate
Durbin-Watson statistic and significance”. Software component
provided by Boston College Department of Economics in its series
Statistical Software Components No. T850802.
DWATSON (SERIES) computes the Durbin-Watson statistic d of serial correlation
and the significance level, if any, at which the null hypothesis d=2 is rejected against
either of the one-sided alternatives (but not both!), using both upper-bound and lower-
bound critical values.
Full module available at:
http://fmwww.bc.edu/repec/bocode/d/dwatson.m
Selected Readings –August 2012 23
3 BOOK
3.1 Durbin James and Koopman Siem Jan, 2012. “Time Series Analysis
by State Space Methods: Second Edition”.
This new edition updates Durbin and Koopman's important text on the state space
approach to time series analysis. The distinguishing feature of state space time series
models is that observations are regarded as made up of distinct components such as
trend, seasonal, regression elements and disturbance terms, each of which is modelled
separately. The techniques that emerge from this approach are very flexible and are
capable of handling a much wider range of problems than the main analytical system
currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions
to this second edition include the filtering of nonlinear and non-Gaussian series. Part I
of the book obtains the mean and variance of the state, of a variable intended to
measure the effect of an interaction and of regression coefficients, in terms of the
observations. Part II extends the treatment to nonlinear and non-normal models. For
these, analytical solutions are not available so methods are based on simulation.
Selected Readings –August 2012 24
4 INTERVIEW
4.1 Phillips Peter C. B., 1988. “The ET Interview: Professor James
Durbin”. Cambridge University Press, Econometric Theory, Volume
4 (1988), Issue 01 (April), Pages 125-157.
No abstract is available.
Full text available at:
http://journals.cambridge.org/action/displayAbstract?fromPage=onlineandaid=790590
9
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