Focus on: James Durbin August 2012

Selected Readings –August 2012 1

SELECTED READINGS

Focus on: James Durbin

August 2012


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


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


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


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


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"

[email protected].

mailto:[email protected]


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.


http://econjwatch.org/file_download/434/HatzinikolauMay2010.pdf

http://arxiv.org/abs/1104.3328

http://econjwatch.org/file_download/434/HatzinikolauMay2010.pdf


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


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.


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.

http://econstor.eu/bitstream/10419/49321/1/384011888.pdf

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=261002


Nevertheless some rough analysis of behaviour for finite samples is included at the

end of paper.


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.



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

http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/100


http://www.tandfonline.com/doi/abs/10.1080/07474939808800423


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.


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.


http://www.sciencedirect.com/science/article/pii/0304407694900906

http://www.sciencedirect.com/



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.



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.



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




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.


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.


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.



http://www.sciencedirect.com/science/article/pii/030440769290031L

http://www.jstor.org/



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.


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.


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.



ftp://zappa.ubvu.vu.nl/19910021.pdf

http://www.sciencedirect.com/science/article/pii/016517659190010I

http://www.sciencedirect.com/science/article/pii/016517659190052M

ftp://zappa.ubvu.vu.nl/19910021.pdf


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.


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.


http://www.sciencedirect.com/science/article/pii/030440769190079S

http://www.sciencedirect.com/science/article/pii/030440769190081N

http://www.sciencedirect.com/science/article/pii/030440769190079S


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.




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.



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





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.



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.



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.



1







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.




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.



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.







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.



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.



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.




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.









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.



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.




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.







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.




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.




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.




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.




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.










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.




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.







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

http://fmwww.bc.edu/repec/bocode/d/durbinh.ado

http://fmwww.bc.edu/repec/bocode/d/dwatson.m


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.


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.




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Documents

Focus on: James Durbin August 2012