On the Distribution of a Statistic Used for Detecting First-Order Serial Correlation

다국어 초록 (Multilingual Abstract)

This paper provides a simple methodology for approximating the distribution of a test statistic proposed by J. Durbin and G. S. Watson. After expressing the statistic as a ratio of quadratic forms, its exact moments are evaluated by making use of a recursive formula. Its density function is then approximated by a beta density function multiplied by a linear combination of Jacobi orthogonal polynomials. The coefficients of the linear combination are determined by making use of a moment-based methodology. An integral representation of the moments of the statistic under the alternative hypothesis is also provided. As verified by a simulation study, the approach used in this paper, which takes into account the observation matrix of explanatory variables associated with the assumed regression model, yields very accurate critical values for testing independence versus first-order serial correlation.

참고문헌 (Reference)

1 정형철, "스플라인 회귀를 활용한 소표본 등화" 한국자료분석학회 6 (6): 825-835, 2004

2 강창완, "붓스트랩방법을 이용한 음이항분포 모수 k의 추정" 한국자료분석학회 5 (5): 519-526, 2003

3 정병철, "붓스트랩 방법을 이용한 분산의 신뢰구간 추정" 한국자료분석학회 7 (7): 871-878, 2005

4 Theil, H., "Testing the independence of regression disturbances" 56 (56): 793-806, 1961

5 Henshaw, R. C., "Testing single-equation least squares regression methods for autocorrelated disturbances" 34 (34): 646-660, 1966

6 Durbin, J., "Testing for serial correlation in least squares regression: I" 37 (37): 409-428, 1950

7 Hannan, E. J., "Testing for serial correlation in least squares regression" 44 (44): 57-66, 1957

8 Durbin, J., "Testing for serial Correlation in least squares regression: III" 58 (58): 1-19, 1971

9 Lieberman, O., "Saddlepoint approximation for the distribution of a ratio of quadratic forms in normal variables" 89 (89): 924-928, 1994

10 Mathai, A. M., "Quadratic Forms in Random Variables, Theory and Applications, Marcel Dekker Inc" New York 1992

11 Cambanis, S., "On the theory of elliptically contoured distributions" 11 (11): 368-385, 1981

12 Provost, S. B, "Moment-based density approximants" 9 (9): 727-756, 2005

13 Hildreth, C., "Demand Relations with Auto-Correlated Disturbances, East Lansing, Michigan: Michigan State University, Agricultural Experiment Station, Department of Agricultural Economics" 276 : 1960

14 Johnson, N. L., "Continuous Univariate Distributions-2" Wiley 1994

15 김대학, "Bootstrap Prediction Interval estimator of SVM" 한국자료분석학회 6 (6): 655-662, 2004

16 Smith, P. J, "A recursive formulation of the old problem of obtaining moments from cumulants and vice versa" 49 (49): 217-219, 1995