TY - JOUR

T1 - Could significant regression be treated as insignificant

T2 - An anomaly in statistics?

AU - Cheng, Yushan

AU - Hui, Yongchang

AU - Liu, Shuangzhe

AU - Wong, Wing Keung

N1 - Funding Information:
This research has been supported by Xi?an Jiaotong University, University of Canberra, Asia University, China Medical University Hospital, The Hang Seng University of Hong Kong, Research Grants Council (RGC) of Hong Kong (project number 12500915), and Ministry of Science and Technology (MOST, Project Numbers 106-2410-H-468-002 and 107-2410-H-468-002-MY3), Taiwan. The authors are grateful to the editor-in-chief, Professor Narayanaswamy Balakrishnan, and anonymous referees for substantive comments that have significantly improved this manuscript. The fourth author thank to Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement.
Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.

PY - 2022

Y1 - 2022

N2 - Literature has found that regression of independent (nearly) nonstationary time series could be spurious. We incorporate this idea to examine whether significant regression could be treated as insignificant in some situations. To do so, we conjecture that significant regression could appear significant in some cases but it could become insignificant in some other cases. To check whether our conjecture could hold, we set up a model in which both dependent and independent variables Yt and Xt are the sum of two variables, say (Formula presented.) and (Formula presented.), in which (Formula presented.) and (Formula presented.) are independent and (nearly) nonstationary AR(1) time series such that (Formula presented.) and (Formula presented.). Following this model-setup, we design some situations and the algorithm for our simulation to check whether our conjecture could hold. We find that on the one hand, our conjecture could hold that significant regression could appear significant in some cases when α 1 and α 2 are of different signs. On the other hand, our findings show that our conjecture does not hold and significant regression cannot be treated as insignificant when α 1 and α 2 are of the same signs. We note that as far as we know, our article is the first article to discover that significant regression can be treated as insignificant in some situations. Thus, the main contribution of our article is that our article is the first article to discover that significant regression can be treated as insignificant in some situations and remains significant in other situations. We believe that our discovery could be an anomaly in statistics. Our findings are useful for academics and practitioners in their data analysis in the way that if they find the regression is insignificant, they should investigate further whether their analysis falls into the problem studied in our article.

AB - Literature has found that regression of independent (nearly) nonstationary time series could be spurious. We incorporate this idea to examine whether significant regression could be treated as insignificant in some situations. To do so, we conjecture that significant regression could appear significant in some cases but it could become insignificant in some other cases. To check whether our conjecture could hold, we set up a model in which both dependent and independent variables Yt and Xt are the sum of two variables, say (Formula presented.) and (Formula presented.), in which (Formula presented.) and (Formula presented.) are independent and (nearly) nonstationary AR(1) time series such that (Formula presented.) and (Formula presented.). Following this model-setup, we design some situations and the algorithm for our simulation to check whether our conjecture could hold. We find that on the one hand, our conjecture could hold that significant regression could appear significant in some cases when α 1 and α 2 are of different signs. On the other hand, our findings show that our conjecture does not hold and significant regression cannot be treated as insignificant when α 1 and α 2 are of the same signs. We note that as far as we know, our article is the first article to discover that significant regression can be treated as insignificant in some situations. Thus, the main contribution of our article is that our article is the first article to discover that significant regression can be treated as insignificant in some situations and remains significant in other situations. We believe that our discovery could be an anomaly in statistics. Our findings are useful for academics and practitioners in their data analysis in the way that if they find the regression is insignificant, they should investigate further whether their analysis falls into the problem studied in our article.

KW - Cointegration

KW - non-stationarity

KW - stationarity

UR - http://www.scopus.com/inward/record.url?scp=85118649439&partnerID=8YFLogxK

U2 - 10.1080/23737484.2021.1986171

DO - 10.1080/23737484.2021.1986171

M3 - Article

AN - SCOPUS:85118649439

VL - 8

SP - 133

EP - 151

JO - Communications in Statistics Case Studies Data Analysis and Applications

JF - Communications in Statistics Case Studies Data Analysis and Applications

SN - 2373-7484

IS - 1

ER -