Robust critical values for unit root tests for series with conditional heteroscedasticity errors: An application of the simple NoVaS transformation

Abstract

In this paper, we introduce a set of critical values for unit root tests that are robust in the presence of conditional heteroscedasticity errors using the normalizing and variance-stabilizing transformation (NoVaS) and examine their properties using Monte Carlo methods. In terms of the size of the test, our analysis reveals that unit root tests with NoVaS-modified critical values have actual sizes close to the nominal size. For the power of the test, we find that unit root tests with NoVaS-modified critical values either have the same power as, or slightly better than, tests using conventional Dickey–Fuller critical values across the sample range considered.

Keywords:

• critical values
• normalizing and variance-stabilizing transformation
• unit root tests

JEL Classification Codes:

• C01
• C12
• C15

Public Interest Statement

Investors anticipate the future return evolution based on their feeling and they respond according to their expectations. They react aggressively or diminish their trading depending on whether they anticipate an increase or a decrease in future returns. Anticipations depend both on over and underconfidence sentiment of investor and on their optimism/pessimism states. This study try to verify whether there’s an asymmetric relationship between investor sentiment and stock market liquidity when investors are more or less over (under) confident and when they are upper-optimistic or upper-pessimistic. Empirical findings confirm the asymmetric response of the stock market liquidity to both overconfidence and optimism–pessimism indicators in the long term. At short term, a rapid asymmetric reaction to over (under) confidence is noticed.

Additional information

Funding

Funding. The authors received no direct funding for this research.

Notes on contributors

Panagiotis Mantalos

Panagiotis Mantalos, PhD, is an associate professor of statistics and econometrics in Department of Economics and Statistics at Linnaeus University, Sweden. His primary field of research deals with the study and development of statistical methodology for diagnostic testing using bootstrap methods. The bootstrap testing method is always assisting for evaluation and building robust models.

His research includes time series, dynamical models in economics, econometrics and financial data econometrics. He has published numerous articles—both theoretical and applied—which can be used to develop strategies for selecting appropriate models. Moreover, using his bootstrap strategies, we can avoid inadequate models, misleading results and incorrect conclusions.