Estimation for Unit Root Testing

We revisit estimation and computation of the Dickey Fuller (DF) and DF-type tests. Firstly, we show that the usual one step approach, based on the "DF autoregression", is likely to be subject to misspecification. Secondly, we clarify a neglected two step approach for estimation of the DF test. (In fact, we introduce a new two step DF autoregression.) This method is always correctly specified and efficient under the circumstances. However, it is either neglected or misused in unit root testing literature. The commonly employed hybrid of the (correct) two step method is shown to be inefficient, even asymptotically. Finally, we further improve/robustify the proposed two step method by employing the missing initial observations. Our finally proposed method is to be used in unit root testing, since it is a new DF autoregression that retains the missing observations.Comment: 10 page

Generalised Pustular Psoriasis (von Zumbusch type) following renal Transplantation. Report of a case and review of the literature

Generalized pustular psoriasis appears as an uncommon variant form of psoriasis consisting of widespread pustules on an erythematous background (von Zumbusch). A 39-year old male patient with a history of plaque psoriasis since the age of 9 who had an acute onset of generalized pustular psoriasis 12 days after he underwent renal transplantation is presented. Despite administered immunosuppression for transplantation the addition of cyclosporine A and methotrexate did not reverse the ongoing process of disease and the patient died on the 57th post-transplant day due to multiorgan failure following severe bone marrow suppression

Nonstationary-Volatility Robust Panel Unit Root Tests and the Great Moderation

This paper argues that typical applications of panel unit root tests should take possible nonstationarity in the volatility process of the innovations of the panel time series into account. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the 'Great Moderation'. It also proposes a new testing approach for panel unit roots that is, unlike many previously suggested tests, robust to such volatility processes. The panel test is based on Simes' (1986) classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor (2008b). The panel test is robust to general patterns of cross-sectional dependence and yet is straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. We use the methods developed here to test for unit roots in OECD panels of gross domestic products and infl ation rates, yielding inference robust to the 'Great Moderation'. We fi nd little evidence of trend stationarity, and mixed evidence regarding inflation stationarity.Die vorliegende Arbeit argumentiert, dass typische Anwendungen von Panel-Einheitswurzeltests die Möglichkeit von Nicht-Stationarität in dem Volatilitätsprozess der Innovationen der Panel-Zeitreihen berücksichtigen sollten. Nicht-stationäre Volatilität entsteht z.B. durch Strukturbrüche in den Varianzen der Innovationen. Ein prominentes Beispiel hierfür ist die Verringerung der Varianzen des BIP-Wachstums vieler Industrieländern, welche unter dem Begriff 'Great Moderation' bekannt ist. Außerdem schlägt die Arbeit einen neuen Testansatz für Panel-Einheitswurzeln vor, der im Gegensatz zu vielen zuvor vorgeschlagen Test robust ist gegenüber solchen Volatilitätsprozessen. Der Panel-Test basiert auf Simes' (1986) klassischem multiplen Testverfahren, welches auf einer Kombination von Zeitreihen-Einheitswurzeltests basiert. Als Zeitreihen-Einheitswurzeltest werden hier die kürzlich vorgeschlagenen Tests von Cavaliere und Taylor (2008b) verwendet. Der Panel-Test ist ebenfalls robust gegenüber allgemeinen Querschnittsabhängigkeitsstrukturen und ist einfach zu implementieren, da lediglich gültig p-Werte von Zeitreihen-Einheitswurzeltests erforderlich sind. Monte Carlo Experimente zeigen, dass andere Panel-Einheitswurzeltests bei Präsenz von nicht-stationärer Volatilität häufig unter starken Verzerrungen leiden, und dass dieser Mangel mit Hilfe des hier vorgeschlagen Verfahrens behoben werden kann. Diese Methode wird hier genutzt, um auf das Vorliegen von Einheitswurzeln in Panels der Bruttoinlandsprodukte und der Inflationsraten von OECD-Ländern zu testen. Dabei werden kaum Anzeichen für Trendstationarität und gemischte Evidenz für Inflations-Stationarität gefunden

On Unit Root Testing with Smooth Transitions

Improved critical values are calculated for Dickey-Fuller-type t ratio unit root tests against trend stationarity about non-linear trend, which is based on one deterministic smooth transition function. Simulation employs finegrid-searchoverbothsmoothtransitionparameterstofind accurate staring values, as well as constrained optimization. In addition, two new parsimonious models are introduced. Finally, an application of the test to the log of Real per capita GNP of USA is provided

Prais-Winsten algorithm for regression with second or higher order autoregressive errors

There is no available Prais-Winsten algorithm for regression with AR(2) or higher order errors, and the one with AR(1) errors is not fully justified or is implemented incorrectly (thus being inefficient). This paper addresses both issues, providing an accurate, computationally fast, and inexpensive generic zig-zag algorithm

Generalized least squares transformation and estimation with autoregressive error

Approximations of the usual GLS transformation matrices are proposed for estimation with AR error that remove boundary discontinuities. The proposed method avoids constrained optimization or rules of thumb that unnecessarily enforce estimated parameters to be in the interior.Gaussian AR model GLS transformation NLS and QML estimation LR test