Spurious Relationship of AR(P) Stable Sequences in Presence of Trends Breaks

Cong YU, Xuefeng WANG, Jifeng MA

Abstract


This paper analyzes spurious regression phenomenon involving AR(p) stable processes with trend breaks. It shows that when those time series are used in ordinary least squares regression, the convenient t-ratios procedures wrongly indicate that the spurious relationship is present as the pair of independent stable series contains trend changes. The spurious relationship becomes stronger as the sample size approaches to infinite. As a result, spurious effects might occur more often than we previously believed as they can arise even between AR(p) stable series in present of trend breaks.


Keywords


Spurious relationship; Stable sequence; T-ratios; Trend breaks

Full Text:

Untitled

References


Avram, F., & Taqqu, M. S. (1986). Weak convergence of moving average with infinite variance. In Dependence in Probability and Statistics, 137-162.

Davis, R. A., & Mikosch, T. (1998). Limit theory for the sample acf of stationary process with heavy tails with applications to ARCH. The Annals of Statistics, 26, 2049-2080.

Granger, C. W. J., Hyung, N., & Jeon, Y. (2001). Spurious regressions with stationary series. Applied Economics, 33, 899-904.

Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2, 111-120.

Hall, P., & Heyde, C. C. (1980). Martingale limit theory and its applications. New York:  Academic.

Jin, H., Tian, Z., & Qin, R. (2009). Bootstrap tests for structural change with infinite variance observations. Statistics and Probability Letters, 79, 1985-1995.

Kokosza, P., & Taqqu M. S. (2001). Can one use the Durbin-Levinson algorithm to generate infinite variance fractional ARIMA time series? Journal of Times Series Analysis, 22, 317-337.

Lizeth, G. B., & Daniel, V. S. (2011). Spurious regression and lurking variables. Statistics & Probability Letters, 81(12), 2004-2011.

Marmol, F. (1998). Spurious regression theory with nonstationary fractionally integrated processes. Journal of Econometrics, 84, 233-250.

Martinez-Rivera, B., Ventosa-Santaulµaria, D. (2012). A comment on “Is the spurious regression problem spurious?” Economics Letters, 115, 229-231.

McElroy, T., & Politis, D. D. (2002). Robust inference for the mean in the presence of serial correlation and heavy-tailed distributions. Econometric Theory, 18(5), 1019-1039.

Mittnik, S., & Rachev, S. T. (2000). Stable paretian models in finance. New York: Wiley.

Phillips, P. C. B. (1986). Understanding spurious regressions in econometrics. Journal of Econometrics, 33, 311-340.

Phillips, P. C. B. (1990). Time series regression with a unit root and infinite variance errors. Econometric Theory, 4, 44-62.

Resnick, S. I. (1986). Point processes regular variation and weak convergence. Advanced in Applied Probability, 18, 66-138.

Tsay, W. J. (1999). Spurious regression between I(1) processes with infinite variance errors. Econometric Theory, 15, 622-628.

Yule, U. (1926). Why do we sometimes get nonsense-correlations between times series? A study in sampling and the nature of time series. Journal of the Royal Statistical Society, 89, 10-13.




DOI: http://dx.doi.org/10.3968%2Fj.ans.1715787020120602.2560

Refbacks

  • There are currently no refbacks.


Reminder

How to do online submission to another Journal?

If you have already registered in Journal A, then how can you submit another article to Journal B? It takes two steps to make it happen:

1. Register yourself in Journal B as an Author

Find the journal you want to submit to in CATEGORIES, click on “VIEW JOURNAL”, “Online Submissions”, “GO TO LOGIN” and “Edit My Profile”. Check “Author” on the “Edit Profile” page, then “Save”.

2. Submission

Go to “User Home”, and click on “Author” under the name of Journal B. You may start a New Submission by clicking on “CLICK HERE”.

We only use the following emails to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
caooc@hotmail.com; office@cscanada.net; office@cscanada.org
ans@cscanada.net;ans@cscanada.org

Copyright © Canadian Research & Development Centre of Sciences and Cultures (CRDCSC)
Address:730, 77e AV, Laval, Quebec, H7V 4A8, Canada

Telephone: 1-514-558 6138
Http://www.cscanada.net; Http://www.cscanada.org
E-mail:caooc@hotmail.com; office@cscanada.net