Could the test from the standard regression model could make significant regression with autoregressive Yt and Xt become insignificant?

Could the test from the standard regression model could make significant regression with autoregressive Yt and Xt become insignificant?

Title

Could the test from the standard regression model could make significant regression with autoregressive Yt and Xt become insignificant?

Authors

• Wing-Keung Wong
  Department of Finance and Big Data Research Center, Asia University
  Department of Medical Research, China Medical University Hospital, Taiwan
  Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University
• Minh Tam Pham
  Department of Finance, College of Management, Asia University

Abstract

This paper extends Cheng, et al. (2022) and Wong and Pham (2022) to investigate whether the statistics TN for testing H0 : β = β0 versus H1 : β ̸= β0 from the traditional regression model from the standard regression model Yt = α + βXt + ut where ut is assumed to be iid N(0, σ2) could be used for regression with autoregressive Yt and Xt. To do so, we set Yt = Y1;t + Y2;t with Y2;t = ϕY Y2;t−1 + et and X2;t = ϕXX2;t−1 + εt in which et i∼id (0, σ2e) and εti ∼id (0, σ2) so that both Yt and Xt are autoregressive. We use the statistics TN for testing H0 : β = β0 versus H1 : β ̸= β0 when the actual β > 0, for example,β = 0.1. In our simulation, we found that the average rejection rate is less than the level of significance for any sample size N smaller than 100. However, for large N, say, N = 1000, the test conrms that the model is significant. Our findings confirm that the test from the standard regression model could make a significant regression with autoregressive noise become insignificant for small sample sizes, but not for very large sample sizes.

Keywords

Stationarity, autoregression, regression, time series analysis, re-gression with autoregressive noise

JEL Classication

C01, C15, C22, C58, C60

How to Cite

Wong, W.-K. & Pham, M. T. (2023). Could the test from the standard regression model could make significant regression with autoregressive Yt and Xt become insignificant?. The International Journal of Finance, 35, 1–19.