Abstract
A new portmanteau test for autocorrelation among the errors of interrupted time-series regression models is proposed. Simulation results demonstrate that the inferential properties of the proposedQ H-M test statistic are considerably more satisfactory than those of the well known Ljung-Box test and moderately better than those of the Box-Pierce test. These conclusions generally hold for a wide variety of autoregressive (AR), moving averages (MA), and ARMA error processes that are associated with time-series regression models of the form described in Huitema and McKean (2000a, 2000b).
Article PDF
Similar content being viewed by others
References
Andrews, D. W. K., &Ploberger, W. (1996). Testing for serial correlation against an ARMA(1,1) process.Journal of the American Statistical Association,91, 1331–1342.
Bowerman, B. L., O’Connell, R. T., &Koehler, A. B. (2005).Forecasting, time series, and regression: An applied approach (4th ed.). Belmont, CA: Thomson, Brooks/Cole.
Box, G. E. P., &Pierce, D. A. (1970). Distribution of residual autocorrelations in autoregressive-integrated moving average time series models.Journal of the American Statistical Association,65, 1509–1526.
Bradley, J. V. (1978). Robustness?British Journal of Mathematical & Statistical Psychology,31, 144–152.
Durbin, J., &Watson, G. S. (1950). Testing for serial correlation in least squares regression: I.Biometrika,37, 409–428.
Durbin, J., &Watson, G. S. (1951). Testing for serial correlation in least squares regression: II.Biometrika,38, 159–178.
Greene, W. H. (2000).Econometric analysis (4th ed.). Upper Saddle River, NJ: Prentice Hall.
Huitema, B. E. (2004). Analysis of interrupted time-series experiments using ITSE: A critique.Understanding Statistics: Statistical Issues in Psychology, Education, & the Social Sciences,3, 27–46.
Huitema, B. E., &McKean, J. W. (1991). Autocorrelation estimation and inference with small samples.Psychological Bulletin,110, 291–304.
Huitema, B. E., &McKean, J. W. (1998). Irrelevant autocorrelation in least-squares intervention models.Psychological Methods,3, 104–116.
Huitema, B. E., &McKean, J. W. (2000a). Design specification issues in time-series intervention models.Educational & Psychological Measurement,60, 38–58.
Huitema, B. E., &McKean, J. W. (2000b). A simple and powerful test for autocorrelated errors in OLS intervention models.Psychological Reports,87, 3–20.
Huitema, B. E., &McKean, J. W. (2007). Identifying autocorrelation generated by various error processes in interrupted time-series regression designs: A comparison of AR1 and portmanteau tests.Educational & Psychological Measurement,67, 447–459.
Huitema, B. E., McKean, J. W., & Laraway, S. (in press). Time-series intervention analysis using ITSACORR: Fatal flaws.Journal of Modern Applied Statistical Methods.
Huitema, B. E., McKean, J. W., & McKnight, S. D. (1994, August).Small-sample time-series intervention analysis: Problems and solutions. Paper presented at the meeting of the American Psychological Association, Los Angeles.
Johnston, J. (1984).Econometric methods (3rd ed.). New York: McGraw-Hill.
Kahaner, D., Moler, C., &Nash, S. (1989).Numerical methods and Software. Englewood Cliffs, NJ: Prentice Hall.
Kutner, M. H., Nachtsheim, C. J., &Neter, J. (2004).Applied linear regression models (4th ed.). New York: McGraw-Hill Irwin.
Ljung, G. M. (1986). Diagnostic testing of univariate time series models.Biometrika,73, 725–730.
Ljung, G. M., &Box, G. E. P. (1978). On a measure of lack of fit in time series models.Biometrika,65, 297–303.
Marsaglia, G., &Bray, T. A. (1964). A convenient method for generating normal variables.SIAM Review,6, 260–264.
McKnight, S., McKean, J. W., &Huitema, B. E. (2000). A double bootstrap method to analyze linear models with autoregressive error terms.Psychological Methods,5, 87–101.
Mills, T. C. (1990).Time series techniques for economists. Cambridge: Cambridge University Press.
Newton, H. J. (1988).TIMESLAB: A Time Series Analysis Laboratory. Pacific Grove, CA: Wadsworth & Brooks/Cole.
Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics,6, 461–464.
Shumway, R. H. (1988).Applied statistical time series analysis. Englewood Cliffs, NJ: Prentice Hall.
White, K. (1993).SHAZAM (Version 7) [Computer software]. Vancouver: University of British Columbia, Department of Economics.
Yaffee, R. A., &McGee, M. (2000).Introduction to time series analysis and forecasting: With applications of SAS and SPSS. San Diego: Academic Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huitema, B.E., McKean, J.W. An improved portmanteau test for autocorrelated errors in interrupted time-series regression models. Behavior Research Methods 39, 343–349 (2007). https://doi.org/10.3758/BF03193002
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03193002