A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. It is shown that members of the family with d < 1 have higher asymptotic local power than the Breitung (2002) test, and when d is small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear timetrend. Furthermore, GLS detrending is shown to improve power when d is small, which is not the case for Breitung's (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with nite sample power that is higher than that of Breitung's (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey-Fuller test with lag length chosen by an information criterion. Terms of use: Documents in JEL Classi cation: C22

A nonparametric unit root test under nonstationary volatility

“…d is fixed to 0.1 as recommended in Nielsen (2009). For formula and asymptotic distribution of MZ s t test see CT.…”

“…So as to modify the Variance Ratio test (Nielsen, 2009) statistic we first need the fractional partial sum operator for some d > 0:…”

“…In the second line we utilize the above formula for fractional binomial coefficients. The third line involves basic operations for fractionally integrated series, which can be found in Nielsen (2009). Finally v k = y k .…”

Nonparametric cointegration analysis of fractional systems with unknown integration orders

“…However, an important di¤erence between d 1 and tuning parameters is that d 1 appears in the asymptotic distribution for n;r (d 1 ). This opens up the possibility of …nding a value of d 1 for which the corresponding test has desirable properties, and Nielsen (2008) argues in favor of d 1 = 0:1 in an asymptotic local power analysis of the univariate variance ratio test. Simulation evidence in section 5 below also supports the choice of d 1 = 0:1 compared to d 1 = 1.…”

Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks

“…The idea of the test was already written in Nielsen (2008) in the univariate case and was thought as nonparametric unit root test. The test could also been adopted in the fractional context as a test for the integration parameter d, as it doesn't assume the knowledge of d to calculate the test statistic.…”