Robinson Kruse

Testing for a break in persistence under long‐range dependencies

We show that tests for a break in the persistence of a time series in the classical I(0)/I(1) framework have serious size distortions when the actual data-generating process (DGP) exhibits long-range dependencies. We prove that the limiting distribution of a CUSUM of squares-based test depends on the true memory parameter if the DGP exhibits long memory. We propose adjusted critical values for the test and give finite sample response curves that allow easy implementation of the test by the practitioner and also ease in computing the relevant critical values. We furthermore prove the consistency of the test for a simple breakpoint estimator also under long memory. We show that the test has satisfying power properties when the correct critical values are used. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd

Changes in persistence, spurious regressions and the Fisher hypothesis

Abstract Declining inflation persistence has been documented in numerous studies. We show that when time series with changes in persistence are analyzed in a regression framework with other persistent time series like interest rates, spurious regressions are likely to occur. We propose the coefficient of determination R2 as a simple test statistic to distinguish between spurious and genuine regressions in situations where time series possibly exhibit changes in persistence. We extend the analysis towards fractional (co-)integration as well. To this end, we establish the limit theory for the R2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. The test performs remarkably well in terms of size and power and is robust to level shifts and multiple changes in persistence. Finally, we apply the test to the Fisher equation for the United States. The newly proposed R2-based test offers robust evidence favourable to the Fisher hypothesis.

Testing for a rational bubble under long memory

We analyse the time series properties of the S&P500 dividend–price ratio in the light of long-memory, structural breaks and rational bubbles. We find an increase in the long-memory parameter in the early 1990s by applying a test recently proposed by Sibbertsen and Kruse [J. Time Series Anal., 2009, 30, 263–285]. An application of the unit root test against long memory of Demetrescu et al. [Econometr. Theory, 2008, 24, 176–215] suggests that the pre-break data can be characterized by long memory, while the post-break sample contains a unit root. These results reconcile two empirical findings that are seen as contradictory: on the one hand, they confirm the existence of fractional integration in the S&P500 log-dividend–price ratio and, on the other, they are consistent with the existence of a rational bubble. The result of a changing memory parameter in the dividend–price ratio has an important implication for the literature on return predictability: the shift from a stationary dividend–price ratio to a unit root process in 1991 is likely to have caused the well-documented failure of conventional return prediction models since the 1990s.

The power of unit root tests against nonlinear local alternatives

This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and nonlinear tests. The foci are (i) on nonlinear smooth transition models and the related nonlinear unit root test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379), and (ii) on the comparison of different adjustment schemes for deterministic terms for the considered nonlinear test. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason for such behavior is the interplay of nonstationarity and nonlinearity. Moreover, we show that the nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the “amount of nonlinearity” of the data generating process), rendering the linear Dickey-Fuller test more powerful than the nonlinear test. Should however the error variance be small, the nonlinear test has better power against local alternatives. The theoretical findings of this paper explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user-specified adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) is far more important for the power of unit root tests than accounting for nonlinearity, at least when the alternative is close to the null.

Interest rate convergence in the EMS prior to European Monetary Union

We analyze the convergence of interest rates in the European Monetary System (EMS) in a novel framework of changing persistence. Due to the specific historical situation in the EMS interest rate differentials were non-stationary before full convergence was achieved. After full convergence has taken place, interest rate differentials became stationary. The applied econometric approach allows us to estimate the exact dates of full convergence endogenously. Our empirical results suggest remarkable differences in the estimated convergence dates for Belgium, France, the Netherlands and Italy which are highly related to steps of European integration policies. We conclude that credibility of monetary policy is of paramount importance for establishing a monetary union successfully. This finding has significant implications for future member states of the EMU.

Unit roots, non-linearities and structural breaks

One of the most infl?uential research ?fields in econometrics over the past decades concerns unit root testing in economic time series. In macro-economics much of the interest in the area originate from the fact that when unit roots are present, then shocks to the time series processes have a persistent effect with resulting policy implications. From a statistical perspective on the other hand, the presence of unit roots has dramatic implications for econometric model building, estimation, and inference in order to avoid the so-called spurious regression problem. The present paper provides a selective review of contributions to the fi?eld of unit root testing over the past three decades. We discuss the nature of stochastic and deterministic trend processes, including break processes, that are likely to affect unit root inference. A range of the most popular unit root tests are presented and their modi?cations to situations with breaks are discussed. We also review some results on unit root testing within the framework of non-linear processes.

A Simple Specification Procedure for the Transition Function in Persistent Nonlinear Time Series Models

A simple procedure for the specification of the transition function describing the regime switch in nonlinear autoregressive models is proposed. This procedure is based on auxiliary regressions of unit root tests and is applicable to a variety of transition functions. In contrast to other procedures, complicated and computer-intense estimation of the candidate models is not necessary. Our approach entirely relies on OLS estimation of auxiliary regressions instead. We use standard information criteria for the selection of the unknown transition function. Our Monte Carlo simulations reveal that the approach works well in practice. Empirical applications to the S&P500 price-earnings ratio and the US interest spread highlight the merits of our suggested procedure.

Explosive behaviour and long memory with an application to European bond yield spreads

This article deals with the interplay of explosive behaviour and long memory. We conduct Monte Carlo simulations and study the finite‐sample properties of the popular unit root test by Phillips et al. (2011) against explosive alternatives. This test exhibits severe upward size distortions under the presence of strongly autocorrelated residuals. We propose the usage of a set of adjusted critical values which leads to a size‐controlled test with increased power. As a complement, we consider the Lagrange Multiplier test against long memory by Tanaka (1999). We study European government bond yield spreads during the financial crisis.