Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels

Abstract

This paper re-evaluates key past results of unit root tests, emphasizing that the use of a conventional level of significance is not in general optimal due to the test having low power. The decision-based significance levels for popular unit root tests, chosen using the line of enlightened judgement under a symmetric loss function, are found to be much higher than conventional ones. We also propose simple calibration rules for the decision-based significance levels for a range of unit root tests. At the decision-based significance levels, many time series in Nelson and Plosser (1982) (extended) data set are judged to be trend-stationary, including real income variables, employment variables and money stock. We also find that nearly all real exchange rates covered in Elliott and Pesavento (2006) study are stationary; and that most of the real interest rates covered in Rapach and Weber (2004) study are stationary. In addition, using a specific loss function, the U.S. nominal interest rate is found to be stationary under economically sensible values of relative loss and prior belief for the null hypothesis.

Interval-Based Hypothesis Testing and Its Applications to Economics and Finance

“…The results for the test of persistence based on the non-inferiority test are largely consistent with those of Kim and Choi (2017) who re-evaluate the ADF test results at the optimal level of significance and report evidence that the real GNP, real per capita GNP, employment, and money stock do not have a unit root. These results are also largely consistent with the Bayesian evidence of Schotman and van Dijk (1991).…”

“…For example, Black (1993) argues that most of investment anomalies identified in finance are likely to be the result of data-mining; while Kandel and Stambaugh (1996) argue that the p-value as measure of evidence often conflicts with economic significance in asset-allocation decisions. Kim and Choi (2017) report that many economically puzzling research outcomes (such as empirical invalidity of the purchasing power parity) based on unit root testing may be the result of incorrectly maintaining the conventional level of significance, despite extremely low power of the test. In behavioral finance, it is a stylized fact that the weather affects stock market (see, for example, Saunders 1993;Hirshleifer and Shumway 2003).…”

“…The most well-known is its low power (at a conventional significance level), which means that there is a high chance of committing Type II error (failure to reject a false null hypothesis). On this point, Kim and Choi (2017) propose the unit root test at the optimal level of significance, which is obtained by minimizing the expected loss from hypothesis testing. They find that the optimal level is in the 0.3 and 0.4 range for many economic time series, arguing that the exclusive use of 0.05 level has led to accumulation of false stylized facts.…”

Significance Testing in Accounting Research: A Critical Evaluation Based on Evidence

“…Simple rules such as the revised standard of evidence (Johnson, ; Benjamin et al, ) and adaptive significance level (Perez and Pericchi, ) should be adopted. Further, the level of significance can be chosen optimally as a function of key factors such as sample size, expected loss, and priors (see Kim and Ji, ; Kim and Choi, ).…”

“…In particular, the level of significance should be set at a much lower level than 0.05 when the sample size is large. When the sample size is small and the power is low, it should be set at a much higher level than 0.05, such as 0.2 or 0.3 (see Kim and Choi, ).…”