Autocorrelation and bias in short time series: An alternative estimator

Quality and Quantity

Volumn 35, Issue 4, 2001, Pages 365-387

  Arnau, Jaume ^a   Bono, Roser ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Autocorrelation; Monte Carlo simulation; Short time series; Statistical power

Indexed keywords

EID: 0035498113     PISSN: 00335177     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012223430234     Document Type: Article

References (50)

1. Anderson, R. L. (1942). Distribution of the serial correlation coefficient. Annals of Mathematical Statistics 13: 1-13.
2. Arnau, J. (1999). Reducción del sesgo en la estimacion de la autocorrelación en series temporales cortas. Metodología de las Ciencias del Comportamiento 1: 25-37.
3. Arnau, J. & Bono, R. (1998). Short time series analysis: C statistic vs Edgington model. Quality and Quantity 32: 63-75.
4. Bartlett, M. S. (1946). On the theoretical specification and sampling properties of autocorrelated time-series. Journal of the Royal Statistical Society 8: 27-41.
5. Bono, R. (1995). Diseños de series temporales interrumpidas: técnicas alternativas de análisis. Doctoral dissertation. Barcelona: Publicacions Universitat de Barcelona.
6. Bono. R. & Arnau, J. (1996). C statistic power analysis through simulation. Psicothema 8: 699-708.
7. Bono. R. & Arnau, J. (1997). Statistic C: Application to behavioral designs. Revista Latinoamericana de Psicología 29: 49-63.
8. Bono, R. & Arnau, J. (1998). Estadístico C: descripción y aplicación a diseños de caso único. Psicológica 19: 27-40.
9. Busk, P. L. & Marascuilo, L. A. (1988). Autocorrelation in single-subject research: A counterargument to the myth of no autocorrelation. Behavioral Assessment 10: 229-242.
10. DeCarlo, L. T. & Tryon, W. W. (1993). Estimating and testing autocorrelation with small samples: A comparison of the C-statistic to a modified estimator. Behavior Research Theory 31: 781-788.
11. Dixon, W. J. (1944). Further contributions to the problem of serial correlation. Annals of Mathematical Statistics 15: 119-144.
12. Forsythe, G. E., Malcolm, M. A. & Moler, C. B. (1977). Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice Hall.
13. Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley.
14. Gentile, J. R., Roden, A. H. & Klein, R. D. (1972). An analysis-of-variance model for the intrasubject replication design. Journal of Applied Behavior Analysis 5: 193-198.
15. Glass, G. V., Willson, V. L. & Gottman, J. M. (1975). Design and Analysis of Time Series Experiments. Boulder: Colorado Associated University Press.
16. Gottman, J. M. (1981). Time-series Analysis: A Comprehensive Introduction for Social Scientists. Cambridge, England: Cambridge University Press.
17. Greenwood, K. M. & Matyas, T. A. (1990). Problems with the application of interrupted time series analysis for brief single-subject data. Behavioral Assessment 12: 355-370.
18. Harrop, J. W. & Velicer, W. F. (1985). A comparison of alternative approaches to the analysis of interrupted time-series. Multivariate Behavioral Research 20: 27-44.
19. Hartmann, D. P. (1974). Forcing square pegs into round holes: Some comments on an analysis of variance model for the intrasubject design. Journal of Applied Behavior Analysis 7: 635-638.
20. Hartmann, D. P., Gottman, J. M., Jones, R. R., Gardner, W., Kazdin, A. E. & Vaught, R. S. (1980). Interrupted time-series analysis and its application to behavioral data. Journal of Applied Behavior Analysis 13: 543-559.
21. Huitema, B. E. (1985). Autocorrelation in applied behavior analysis: A myth. Behavioral Assessment 7: 107-118.
22. Huitema, B. E. (1986). Autocorrelation in behavior modification data: Wherefore art thou?. In A. Poling & R. W. Fuqua (eds), Research Methods in Applied Behavior Analysis: Issues and Advances. New York: Plenum Press, pp. 187-208.
23. Huitema, B. E. (1988). Autocorrelation: 10 years of confusion. Behavioral Assessment 10: 253-294.
24. Huitema, B. E. & McKean, J. W. (1991). Autocorrelation estimation and inference with small samples. Psychological Bulletin 110: 291-304.
25. Huitema, B. E. & McKean, J. W. (1994a). Reduced bias autocorrelation estimation: three jackknife methods. Educational and Psychological Measurement 54: 654-665.
26. F2. Perceptual and Motor Skills 78: 323-330.
27. F2. Perceptual and Motor Skills 78: 331-336.
28. Q2. Educational and Psychological Measurement 56: 232-240.
29. International Mathematical and Statistical Libraries, Inc. (1989). IMSL Library 3. Houston, TX: Author.
30. Jones, R. R., Vaught, R. S. & Weinrott, M. (1977). Time-series analysis in operant research. Journal of Applied Behavior Analysis 10: 151-166.
31. Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation. Biometrika 41: 403-404.
32. Keselman, H. J. & Leventhal, L. (1974). Concerning the statistical procedures enumerated by Gentile et al.: Another perspective. Journal of Applied Behavior Analysis 7: 643-645.
33. Kratochwill, T. R., Aldin, K., Demuth, D., Dawson, D. L., Panicucci, C., Arnston, P., McMurray, N., Hempstead, J. & Levin, J. (1974). A further consideration in the application of an analysis-of-variance model for the intrasubject replication design. Journal of Applied Behavior Analysis 7: 629-634.
34. Marriott, F. H. C. & Pope, J. A. (1954). Bias in the estimation of autocorrelation. Biometrika 41: 390-402.
35. MATLAB. (1998). The Language of Technical Computing (version 5.2). Natick, MA: The Math-Works, Inc.
36. Matyas, T. A. & Greenwood, K. M. (1991). Problems in the estimation of autocorrelation in brief time series and some implications for behavioral data. Behavioral Assessment 13: 137-157.
37. McCleary, R. & Hay, R. A., Jr. (1980). Applied Time Series Analysis for the Social Sciences. Beverly Hills, CA: Sage.
38. McKean, J. W. & Huitema, B. E. (1993). Small sample properties of the Spearman autocorrelation estimator. Perceptual and Motor Skills 76: 38-4-386.
39. Moran, P. A. P. (1948). Some theorems on Time Series II. The significance of the serial correlation coefficient. Biometrika 35: 255-260.
40. SAS Institute Inc. (1990). SAS Language: Reference (version 6, First Ed.). Cary, NC: Author.
41. Scheffé, H. (1959). The Analysis of Variance. New York: Wiley.
42. Sharpley, C. F. & Alavosius, M. P. (1988). Autocorrelation in behavioral data: An alternative perspective. Behavioral Assessment 10: 243-251.
43. Shine, L. C. & Bower, S. M. (1971). A one-way analysis of variance for single-subject designs. Educational and Psychological Measurement 31: 105-113.
44. Simonton, D. K. (1977). Cross-sectional time-series experiments: Some suggested statistical analyses. Psychological Bulletin 84: 489-502.
45. Suen, H. K. (1987). On the epistemology of autocorrelation in applied behavior analysis. Behavioral Assessment 9: 113-124.
46. Suen, H. K. & Ary, D. (1987). Autocorrelation in applied behavior analysis: Myth or reality?. Behavioral Assessment 9: 125-130.
47. Thorensen, C. E. & Elashoff, J. D. (1974). An analysis of variance model for intrasubject replication design: Some additional comments. Journal of Applied Behavior Analysis 7: 639-641.
48. Velicer, W. F. & Harrop, J. W. (1983). The reliability and accuracy of the time-series model identification. Evaluation Review 7: 551-560.
49. Velicer, W. F. & McDonald, R. P. (1984). Time series analysis without model identification. Multivariate Behavioral Research 19: 33-47.
50. Velicer, W. F. & McDonald, R. P. (1991). Cross-sectional time series designs: A general transformation approach. Multivariate Behavioral Research 26: 247-254.