Statistical analysis of discrete-valued time series using categorical ARMA models
This paper concerns the analysis of discrete-valued time series using a class of categorical ARMA models recently proposed by Biswas and Song (2009). Such ARMA processes are flexible to model discrete-valued time series, allowing a wide range of marginal distributions such as binomial, multinomial, Poisson and nominal/ordinal categorical probability mass functions. To apply these models in the data analysis this paper focuses on the development of a needed statistical toolbox, which includes maximum likelihood estimation and inference, model selection, and goodness-of-fit test. Particularly in AR models a bias-corrected AIC statistic is derived for the order selection, while a randomized conditional moment (RCM) test is furnished to examine the goodness-of-fit. Finite-sample performances of the proposed methods are examined through simulation studies, in which the bias-corrected AIC is shown to outperform the traditional AIC and BIC statistics and the RCM test achieves desirable power. As part of the numeric illustration, a data analysis of categorical time series on infant sleep quality is provided by the application of this new toolbox.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bierens, H.J. & Ploberger, W., 1995.
"Asymptotic theory of integrated conditional moment tests,"
1995-124, Tilburg University, Center for Economic Research.
- Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- Bierens, H.J., 1989.
"A consistent conditional moment test of functional form,"
Serie Research Memoranda
0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
- Donald W.K. Andrews & Werner Ploberger, 1992.
"Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative,"
Cowles Foundation Discussion Papers
1015, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
- Biswas, Atanu & Song, Peter X.-K., 2009. "Discrete-valued ARMA processes," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1884-1889, September.
- Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
- de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
- Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer, vol. 92(3), pages 319-341, August.
- Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:112-124. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.