Testing the stability of the functional autoregressive process
The functional autoregressive process has become a useful tool in the analysis of functional time series data. It is defined by the equation , in which the observations Xn and errors [epsilon]n are curves, and is an operator. To ensure meaningful inference and prediction based on this model, it is important to verify that the operator does not change with time. We propose a method for testing the constancy of against a change-point alternative which uses the functional principal component analysis. The test statistic is constructed to have a well-known asymptotic distribution, but the asymptotic justification of the procedure is very delicate. We develop a new truncation approach which together with Mensov's inequality can be used in other problems of functional time series analysis. The estimation of the principal components introduces asymptotically non-negligible terms, which however cancel because of the special form of our test statistic (CUSUM type). The test is implemented using the R package fda, and its finite sample performance is examined by application to credit card transaction data.
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.
Volume (Year): 101 (2010)
Issue (Month): 2 (February)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 1999. "Testing for Changes in Multivariate Dependent Observations with an Application to Temperature Changes," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 96-119, January.
- Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687.
- P. M. Robinson, 1998. "Inference-Without-Smoothing in the Presence of Nonparametric Autocorrelation," Econometrica, Econometric Society, vol. 66(5), pages 1163-1182, September.
- Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
- Kargin, V. & Onatski, A., 2008.
"Curve forecasting by functional autoregression,"
Journal of Multivariate Analysis,
Elsevier, vol. 99(10), pages 2508-2526, November.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
- Donald W.K. Andrews & Christopher J. Monahan, 1990.
"An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,"
Cowles Foundation Discussion Papers
942, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
- Gabrys, Robertas & Kokoszka, Piotr, 2007. "Portmanteau Test of Independence for Functional Observations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1338-1348, December.
- Hansen, Bruce E., 1995.
"Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power,"
Cambridge University Press, vol. 11(05), pages 1148-1171, October.
- Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
- Peter Hall & Mohammad Hosseini-Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:352-367. 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: (Dana Niculescu)
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.